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Dr. Gómez Aguilar José Francisco
CONACyT - Jóvenes Investigadores, Departamento de Ingeniería Electrónica, Centro Nacional de Investigación y Desarrollo Tecnológico, Tecnológico Nacional de México, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, México

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0 Nonlinear Dynamics
0 Process Control
0 Signal Processing
0 fractional calculus
0 mathematical models

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Fractional differential equations
fractional calculus
Chaos
mathematical models
Numerical schemes
Process Control
Signal Processing

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Journal article
Published: 28 August 2021 in Mathematics
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In this paper, we study the recently proposed fractional-order operators with general analytic kernels. The kernel of these operators is a locally uniformly convergent power series that can be chosen adequately to obtain a family of fractional operators and, in particular, the main existing fractional derivatives. Based on the conditions for the Laplace transform of these operators, in this paper, some new results are obtained—for example, relationships between Riemann–Liouville and Caputo derivatives and inverse operators. Later, employing a representation for the product of two functions, we determine a form of calculating its fractional derivative; this result is essential due to its connection to the fractional derivative of Lyapunov functions. In addition, some other new results are developed, leading to Lyapunov-like theorems and a Lyapunov direct method that serves to prove asymptotic stability in the sense of the operators with general analytic kernels. The FOB-stability concept is introduced, which generalizes the classical Mittag–Leffler stability for a wide class of systems. Some inequalities are established for operators with general analytic kernels, which generalize others in the literature. Finally, some new stability results via convex Lyapunov functions are presented, whose importance lies in avoiding the calculation of fractional derivatives for the stability analysis of dynamical systems. Some illustrative examples are given.

ACS Style

Oscar Martínez-Fuentes; Fidel Meléndez-Vázquez; Guillermo Fernández-Anaya; José Francisco Gómez-Aguilar. Analysis of Fractional-Order Nonlinear Dynamic Systems with General Analytic Kernels: Lyapunov Stability and Inequalities. Mathematics 2021, 9, 2084 .

AMA Style

Oscar Martínez-Fuentes, Fidel Meléndez-Vázquez, Guillermo Fernández-Anaya, José Francisco Gómez-Aguilar. Analysis of Fractional-Order Nonlinear Dynamic Systems with General Analytic Kernels: Lyapunov Stability and Inequalities. Mathematics. 2021; 9 (17):2084.

Chicago/Turabian Style

Oscar Martínez-Fuentes; Fidel Meléndez-Vázquez; Guillermo Fernández-Anaya; José Francisco Gómez-Aguilar. 2021. "Analysis of Fractional-Order Nonlinear Dynamic Systems with General Analytic Kernels: Lyapunov Stability and Inequalities." Mathematics 9, no. 17: 2084.

Journal article
Published: 18 August 2021
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In this article, a mathematical model for hypertensive or diabetic patients open to COVID-19 is considered along with a set of first-order nonlinear differential equations. Moreover, the method of piecewise arguments is used to discretize the continuous system. The mathematical system is said to reveal six equilibria, namely, extinction equilibrium, boundary equilibrium, quarantined-free equilibrium, exposure-free equilibrium, endemic equilibrium, and the equilibrium free from susceptible population. Local stability conditions are developed for our discrete-time mathematical system about each of its equilibrium point. The existence of period-doubling bifurcation and chaos is studied in the absence of isolated population. It is shown that our system will become unstable and experiences the chaos when the quarantined compartment is empty, which is true in biological meanings. The existence of Neimark–Sacker bifurcation is studied for the endemic equilibrium point. Moreover, it is shown numerically that our discrete-time mathematical system experiences the period-doubling bifurcation about its endemic equilibrium. To control the period-doubling bifurcation, Neimark–Sacker bifurcation, a generalized hybrid control methodology is used. Moreover, this model is analyzed along with generalized hybrid control in order to eliminate chaos and oscillation epidemiologically presenting the significance of quarantine in the COVID-19 environment.

ACS Style

Muhammad Salman Khan; Maria Samreen; Muhammad Ozair; Takasar Hussain; J. F. Gómez-Aguilar. Bifurcation analysis of a discrete-time compartmental model for hypertensive or diabetic patients exposed to COVID-19. 2021, 136, 1 .

AMA Style

Muhammad Salman Khan, Maria Samreen, Muhammad Ozair, Takasar Hussain, J. F. Gómez-Aguilar. Bifurcation analysis of a discrete-time compartmental model for hypertensive or diabetic patients exposed to COVID-19. . 2021; 136 (8):1.

Chicago/Turabian Style

Muhammad Salman Khan; Maria Samreen; Muhammad Ozair; Takasar Hussain; J. F. Gómez-Aguilar. 2021. "Bifurcation analysis of a discrete-time compartmental model for hypertensive or diabetic patients exposed to COVID-19." 136, no. 8: 1.

Research article
Published: 12 August 2021 in Fractals
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This paper introduces a fractional-order financial risk system for the first time. Employing well-known tools and analyses such as bifurcations diagrams and spectral entropy, the dynamical behaviors of the system associated with fractional derivative are investigated. The impacts of the fractional derivative on the system’s behavior and its dynamical feature are shown. Then, tracking control and stabilization of the systems are studied. As it is obvious, the existence of faults and failures in the process of control of financial and economic systems is undeniable — this issue necessitates applying proper control techniques for the systems. So as to achieve appropriate results in the control of fractional financial risk system, two finite-time fault-tolerant controllers are proposed, namely, finite-time active fault-tolerant control and finite-time passive fault-tolerant control. Not only do these techniques force the system to reach desired values in finite time, but also, the proposed techniques are robust against uncertainties, faults, and failures in actuators. Through finite-time observers, the effects of all uncertainties are taken to account in the active controller. Finally, numerical simulations of tracking control and stabilization are presented. For numerical simulations, the fractional financial risk system is considered to be in the presence of unknown disturbance as well as faults and failures in actuators. It is assumed that the system is in the presence of various types of actuator faults. Numerical results affirm the ability of the offered control techniques for pushing the states of the fractional-order risk system to the desired value in a short period of time.

ACS Style

Bo Wang; Hadi Jahanshahi; Stelios Bekiros; Yu-Ming Chu; J. F. Gómez-Aguilar; Fawaz E. Alsaadi; Madini O. Alassafi. TRACKING CONTROL AND STABILIZATION OF A FRACTIONAL FINANCIAL RISK SYSTEM USING NOVEL ACTIVE FINITE-TIME FAULT-TOLERANT CONTROLS. Fractals 2021, 1 .

AMA Style

Bo Wang, Hadi Jahanshahi, Stelios Bekiros, Yu-Ming Chu, J. F. Gómez-Aguilar, Fawaz E. Alsaadi, Madini O. Alassafi. TRACKING CONTROL AND STABILIZATION OF A FRACTIONAL FINANCIAL RISK SYSTEM USING NOVEL ACTIVE FINITE-TIME FAULT-TOLERANT CONTROLS. Fractals. 2021; ():1.

Chicago/Turabian Style

Bo Wang; Hadi Jahanshahi; Stelios Bekiros; Yu-Ming Chu; J. F. Gómez-Aguilar; Fawaz E. Alsaadi; Madini O. Alassafi. 2021. "TRACKING CONTROL AND STABILIZATION OF A FRACTIONAL FINANCIAL RISK SYSTEM USING NOVEL ACTIVE FINITE-TIME FAULT-TOLERANT CONTROLS." Fractals , no. : 1.

Special issue paper
Published: 04 August 2021 in Mathematical Methods in the Applied Sciences
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It is eminent that iterative learning control algorithm is of high significance due to its speciality of tracking control for systems developed from real-world phenomena that occurs repeatedly. Singular systems are well-known for their applications in network analysis, biological systems, economic systems, social systems, engineering systems, time-series analysis, and many other areas of science and technology. In this article, we investigate and analyze the convergence characteristic of PD-type iterative learning control (ILC) scheme for linear discrete-time singular system. We reformulate the discrete-time singular system as a kind of algebraic input-output transmission based on the lifted vector technique. The monotonic convergence has been deduced in the sense of 2-norm for the first-order as well as second-order PD-type ILC scheme. It is shown that the second-order PD-type ILC algorithm has good tracking performance than the first-order on the whole time interval. Finally, we perform comparative analysis to validate the results numerically.

ACS Style

Shahzad Khattak; Ijaz Hussain; José Francisco Gomez‐Aguilar; Rashid Jan. Analysis of PD‐type iterative learning control for discrete‐time singular system. Mathematical Methods in the Applied Sciences 2021, 1 .

AMA Style

Shahzad Khattak, Ijaz Hussain, José Francisco Gomez‐Aguilar, Rashid Jan. Analysis of PD‐type iterative learning control for discrete‐time singular system. Mathematical Methods in the Applied Sciences. 2021; ():1.

Chicago/Turabian Style

Shahzad Khattak; Ijaz Hussain; José Francisco Gomez‐Aguilar; Rashid Jan. 2021. "Analysis of PD‐type iterative learning control for discrete‐time singular system." Mathematical Methods in the Applied Sciences , no. : 1.

Original paper
Published: 18 July 2021 in International Journal of Circuit Theory and Applications
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In the presented work, we present an accurate procedure, which is the spectral method, to find a solution to a certain class of the very important fractional (described by the Liouville–Caputo sense) models of the electrical RL, RC, and RLC circuits. This method is collocated using some important advantages of the generalized Legendre polynomials to obtain the numerical solution for these models. Besides, we compare the approximate solutions that are obtained using the presented technique for the proposed models with their exact solution in the given numerical examples.

ACS Style

M. M. Khader; J. F. Gómez‐Aguilar; M. Adel. Numerical study for the fractional RL, RC, and RLC electrical circuits using Legendre pseudo‐spectral method. International Journal of Circuit Theory and Applications 2021, 1 .

AMA Style

M. M. Khader, J. F. Gómez‐Aguilar, M. Adel. Numerical study for the fractional RL, RC, and RLC electrical circuits using Legendre pseudo‐spectral method. International Journal of Circuit Theory and Applications. 2021; ():1.

Chicago/Turabian Style

M. M. Khader; J. F. Gómez‐Aguilar; M. Adel. 2021. "Numerical study for the fractional RL, RC, and RLC electrical circuits using Legendre pseudo‐spectral method." International Journal of Circuit Theory and Applications , no. : 1.

Preprint content
Published: 09 July 2021
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Nonlinear fractional order partial differential equations standing for the numerous dynamical systems relating to nature world are supposed to by unraveled for depicting complex physical phenomena. In this exploration, we concentrate to disentangle the space and time fractional nonlinear Schrodinger equation, Korteweg-De Vries (KdV) equation and the Wazwaz-Benjamin-Bona-Mahony (WBBM) equation bearing the noteworthy significance in accordance to their respective position. A composite wave variable transformation with the assistance of conformable fractional derivative transmutes the declared equations to ordinary differential equations. A successful implementation of the proposed improved auxiliary equation technique collects enormous wave solutions in the form of exponential, rational, trigonometric and hyperbolic functions. The found solutions involving many free parameters under consideration of particular values are figured out which appeared in different shape as kink type, anti-kink type, singular kink type, bell shape, anti-bell shape, singular bell shape, cuspon, peakon, periodic etc. The performance of the proposed scheme shows its potentiality through construction of fresh and further general exact traveling wave solutions of three nonlinear equations. A comparison of the achieved outcomes in this investigation with the results found in the literature ensures the diversity and novelty of ours. Consequently, the improved auxiliary equation technique stands as efficient and concise tool which deserves further use to unravel any other nonlinear evolution equations arise in various physical sciences like applied mathematics, mathematical physics and engineering.

ACS Style

Tarikul Islam; Francisco Gomez; Ali Akbar. Diverse Soliton Structures for Fractional Nonlinear Schrodinger Equation, KdV Equation and WBBM Equation Adopting a New Technique. 2021, 1 .

AMA Style

Tarikul Islam, Francisco Gomez, Ali Akbar. Diverse Soliton Structures for Fractional Nonlinear Schrodinger Equation, KdV Equation and WBBM Equation Adopting a New Technique. . 2021; ():1.

Chicago/Turabian Style

Tarikul Islam; Francisco Gomez; Ali Akbar. 2021. "Diverse Soliton Structures for Fractional Nonlinear Schrodinger Equation, KdV Equation and WBBM Equation Adopting a New Technique." , no. : 1.

Special issue paper
Published: 20 June 2021 in Mathematical Methods in the Applied Sciences
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In this article, we study existence, uniqueness, and stability analysis in Hyer–Ulam settings of delay fractional differential equations with nonlinear singular p-Laplacian operator ϕp. The fractional operators are taken in the Caputo sense. The fractional differential equation is converted into an integral form with the Green's theorem, also a fixed point approach is studied for this article. We include an example with specific parameter and assumptions to show the results of the proposal. Our results generalize some of the works in the literature.

ACS Style

Muhammad Aslam; José Francisco Gómez‐Aguilar; Ghaus Ur‐Rahman; Rashid Murtaza. Existence, uniqueness, and Hyers–Ulam stability of solutions to nonlinear p ‐Laplacian singular delay fractional boundary value problems. Mathematical Methods in the Applied Sciences 2021, 1 .

AMA Style

Muhammad Aslam, José Francisco Gómez‐Aguilar, Ghaus Ur‐Rahman, Rashid Murtaza. Existence, uniqueness, and Hyers–Ulam stability of solutions to nonlinear p ‐Laplacian singular delay fractional boundary value problems. Mathematical Methods in the Applied Sciences. 2021; ():1.

Chicago/Turabian Style

Muhammad Aslam; José Francisco Gómez‐Aguilar; Ghaus Ur‐Rahman; Rashid Murtaza. 2021. "Existence, uniqueness, and Hyers–Ulam stability of solutions to nonlinear p ‐Laplacian singular delay fractional boundary value problems." Mathematical Methods in the Applied Sciences , no. : 1.

Preprint content
Published: 15 June 2021
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The objective of this research is to study the collective variable (CV) technique to explore an important form of Schrödinger equation known as the Gerdjikov-Ivanov (GI) equation which expresses the dynamics of solitons for optical fibers in terms of pulse parameters. These parameters are temporal position, amplitude, width, chirp, phase, and frequency known as collective variables (CVs). This is an effective and dynamic mathematical gadget to obtain soliton solutions of non-dimensional as well as perturbed GI equations. Moreover, an established numerical scheme that is the fourth-order Runge-Kutta method is exerted for the numerical simulation of the revealing coupled system of six ordinary differential equations which represent all the CVs included in the pulse ansatz. The CV approach is used to determine the evolution of pulse parameters with the propagation distance and illustrated it illustrated it graphically. Furthermore, Figures show the compelling periodic oscillations of pulse chirp, width, frequency and amplitude of soliton. For various values of super-Gaussian pulse parameters, the numerical behavior of solitons to illustrate variations in CVs is provided. Other significant aspects with regards to the current investigation are also inferred.

ACS Style

Zara Hassan; Nauman Raza; Francisco Gomez. Novel Optical Solitons to the Perturbed Gerdjikov-Ivanov Equation Via Collective Variables. 2021, 1 .

AMA Style

Zara Hassan, Nauman Raza, Francisco Gomez. Novel Optical Solitons to the Perturbed Gerdjikov-Ivanov Equation Via Collective Variables. . 2021; ():1.

Chicago/Turabian Style

Zara Hassan; Nauman Raza; Francisco Gomez. 2021. "Novel Optical Solitons to the Perturbed Gerdjikov-Ivanov Equation Via Collective Variables." , no. : 1.

Journal article
Published: 04 June 2021 in Mathematical Modelling of Natural Phenomena
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In this paper, we implemented the generalized (G′/G) and extended (G′/G) methods to solve fractional-order biological population models. The fractional-order derivatives are represented by the Caputo operator. The solutions of some illustrative examples are presented to show the validity of the proposed method. First, the transformation is used to reduce the given problem into ordinary differential equations. The ordinary differential equation is than solve by using modified (G′/G) method. Different families of traveling waves solutions are constructed to explain the different physical behavior of the targeted problems. Three important solutions, hyperbolic, rational and periodic, are investigated by using the proposed techniques. The obtained solutions within different classes have provided effective information about the targeted physical procedures. In conclusion, the present techniques are considered the best tools to analyze different families of solutions for any fractional-order problem.

ACS Style

Hassan Khan; Rasool Shah; J.F. Gómez-Aguilar; Shoaib; Dumitru Baleanu; Poom Kumam. Travelling waves solution for fractional-order biological population model. Mathematical Modelling of Natural Phenomena 2021, 16, 32 .

AMA Style

Hassan Khan, Rasool Shah, J.F. Gómez-Aguilar, Shoaib, Dumitru Baleanu, Poom Kumam. Travelling waves solution for fractional-order biological population model. Mathematical Modelling of Natural Phenomena. 2021; 16 ():32.

Chicago/Turabian Style

Hassan Khan; Rasool Shah; J.F. Gómez-Aguilar; Shoaib; Dumitru Baleanu; Poom Kumam. 2021. "Travelling waves solution for fractional-order biological population model." Mathematical Modelling of Natural Phenomena 16, no. : 32.

Accepted manuscript
Published: 04 June 2021 in Physica Scripta
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This research considers an inverse source problem for fractional diusion equation, containing fractional derivative with non-singular and non-local kernel, namely, Atangana-Baleanu fractional derivative. In our study, an explicit solution set is acquired via the expansion method and the overdetermination condition at a nal time. The problem is ill-posed in the meaning of Hadamard and thus the solution does not continuously depend on the input data. We have applied the Tikhonov regularization method to regularize the unstable solution. For the estimation of convergence between the exact and the regularized solutions, we focus on two parameter choice rules, a-prioi and a-posteriori parameter.

ACS Style

Smina Djennadi; Nabil Shawagfeh; Mustafa Inc; Mohamed S. Osman; J.F. Gómez-Aguilar; Omar Abu Arqub. The Tikhonov regularization method for the inverse source problem of time fractional heat equation in the view of ABC-fractional technique. Physica Scripta 2021, 96, 094006 .

AMA Style

Smina Djennadi, Nabil Shawagfeh, Mustafa Inc, Mohamed S. Osman, J.F. Gómez-Aguilar, Omar Abu Arqub. The Tikhonov regularization method for the inverse source problem of time fractional heat equation in the view of ABC-fractional technique. Physica Scripta. 2021; 96 (9):094006.

Chicago/Turabian Style

Smina Djennadi; Nabil Shawagfeh; Mustafa Inc; Mohamed S. Osman; J.F. Gómez-Aguilar; Omar Abu Arqub. 2021. "The Tikhonov regularization method for the inverse source problem of time fractional heat equation in the view of ABC-fractional technique." Physica Scripta 96, no. 9: 094006.

Regular article
Published: 31 May 2021 in The European Physical Journal Plus
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Since December 2019, the new coronavirus has raged in China and subsequently all over the world. From the first days, researchers have tried to discover vaccines to combat the epidemic. Several vaccines are now available as a result of the contributions of those researchers. As a matter of fact, the available vaccines should be used in effective and efficient manners to put the pandemic to an end. Hence, a major problem now is how to efficiently distribute these available vaccines among various components of the population. Using mathematical modeling and reinforcement learning control approaches, the present article aims to address this issue. To this end, a deterministic Susceptible-Exposed-Infectious-Recovered-type model with additional vaccine components is proposed. The proposed mathematical model can be used to simulate the consequences of vaccination policies. Then, the suppression of the outbreak is taken to account. The main objective is to reduce the effects of Covid-19 and its domino effects which stem from its spreading and progression. Therefore, to reach optimal policies, reinforcement learning optimal control is implemented, and four different optimal strategies are extracted. Demonstrating the efficacy of the proposed methods, finally, numerical simulations are presented.

ACS Style

Alireza Beigi; Amin Yousefpour; Amirreza Yasami; J. F. Gómez-Aguilar; Stelios Bekiros; Hadi Jahanshahi. Application of reinforcement learning for effective vaccination strategies of coronavirus disease 2019 (COVID-19). The European Physical Journal Plus 2021, 136, 1 -22.

AMA Style

Alireza Beigi, Amin Yousefpour, Amirreza Yasami, J. F. Gómez-Aguilar, Stelios Bekiros, Hadi Jahanshahi. Application of reinforcement learning for effective vaccination strategies of coronavirus disease 2019 (COVID-19). The European Physical Journal Plus. 2021; 136 (5):1-22.

Chicago/Turabian Style

Alireza Beigi; Amin Yousefpour; Amirreza Yasami; J. F. Gómez-Aguilar; Stelios Bekiros; Hadi Jahanshahi. 2021. "Application of reinforcement learning for effective vaccination strategies of coronavirus disease 2019 (COVID-19)." The European Physical Journal Plus 136, no. 5: 1-22.

Research article
Published: 27 May 2021 in Mathematical Methods in the Applied Sciences
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In this paper, a modified nonlinear Schrödinger equation with spatiotemporal dispersion is formulated in the senses of Caputo fractional derivative and conformable derivative. A new generalized double Laplace transform coupled with Adomian decomposition method has been defined and applied to solve the newly formulated nonlinear Schrödinger equation with spatiotemporal dispersion. The approximate analytical solutions are obtained and compared with each other graphically.

ACS Style

Mohammed K. A. Kaabar; Francisco Martínez; José Francisco Gómez‐Aguilar; Behzad Ghanbari; Melike Kaplan; Hatira Günerhan. New approximate analytical solutions for the nonlinear fractional Schrödinger equation with second‐order spatio‐temporal dispersion via double Laplace transform method. Mathematical Methods in the Applied Sciences 2021, 44, 11138 -11156.

AMA Style

Mohammed K. A. Kaabar, Francisco Martínez, José Francisco Gómez‐Aguilar, Behzad Ghanbari, Melike Kaplan, Hatira Günerhan. New approximate analytical solutions for the nonlinear fractional Schrödinger equation with second‐order spatio‐temporal dispersion via double Laplace transform method. Mathematical Methods in the Applied Sciences. 2021; 44 (14):11138-11156.

Chicago/Turabian Style

Mohammed K. A. Kaabar; Francisco Martínez; José Francisco Gómez‐Aguilar; Behzad Ghanbari; Melike Kaplan; Hatira Günerhan. 2021. "New approximate analytical solutions for the nonlinear fractional Schrödinger equation with second‐order spatio‐temporal dispersion via double Laplace transform method." Mathematical Methods in the Applied Sciences 44, no. 14: 11138-11156.

Journal article
Published: 19 May 2021 in Results in Physics
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In this paper, we investigate the fractional epidemic mathematical model and dynamics of COVID-19. The Wuhan city of China is considered as the origin of the corona virus. The novel corona virus is continuously spread its range of effectiveness in nearly all corners of the world. Here we analyze that under what parameters and conditions it is possible to slow the speed of spreading of corona virus. We formulate a transmission dynamical model where it is assumed that some portion of the people generates the infections, which is affected by the quarantine and latent time. We study the effect of various parameters of corona virus through the fractional mathematical model. The Laguerre collocation technique is used to deal with the concerned mathematical model numerically. In order to deal with the dynamics of the novel corona virus we collect the experimental data from 15th–21st April, 2020 of Maharashtra state, India. We analyze the effect of various parameters on the numerical solutions by graphical comparison for fractional order as well as integer order. The pictorial presentation of the variation of different parameters used in model are depicted for upper and lower solution both.

ACS Style

Prashant Pandey; Yu-Ming Chu; J.F. Gómez-Aguilar; Hadi Jahanshahi; Ayman A. Aly. A novel fractional mathematical model of COVID-19 epidemic considering quarantine and latent time. Results in Physics 2021, 26, 104286 -104286.

AMA Style

Prashant Pandey, Yu-Ming Chu, J.F. Gómez-Aguilar, Hadi Jahanshahi, Ayman A. Aly. A novel fractional mathematical model of COVID-19 epidemic considering quarantine and latent time. Results in Physics. 2021; 26 ():104286-104286.

Chicago/Turabian Style

Prashant Pandey; Yu-Ming Chu; J.F. Gómez-Aguilar; Hadi Jahanshahi; Ayman A. Aly. 2021. "A novel fractional mathematical model of COVID-19 epidemic considering quarantine and latent time." Results in Physics 26, no. : 104286-104286.

Originalpaper
Published: 01 May 2021 in Programming and Computer Software
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The registration of a 3D model over an image can be seen as the alignment of visual correspondences extracted from these two data. This is a challenging task and it is even more complex when the two images have a different modality. This paper introduces an approach that allows matching features detected in two different modalities: photographs and 3D models, by using a common 2D representation. Our approach is based on a modification of the Marching Cubes algorithm aiming to remove ambiguous cases without adding further calculations in each cube. We share the idea about the crucial importance of splitting the equivalence cases into two classes. Considering all the possible states inside/outside in the four corners of a cube side, indeed, there are only four non-trivial cases after eliminating those equivalences through the rotation. The obtained results allow us to validate the feasibility of the proposed methodology.

ACS Style

Delia Irazú Hernández Farías; Rafael Guzmán Cabrera; Teodoro Cordova Fraga; José Zacarías Huamaní Luna; Jose Francisco Gomez Aguilar. Modification of the Marching Cubes Algorithm to Obtain a 3D Representation of a Planar Image. Programming and Computer Software 2021, 47, 215 -223.

AMA Style

Delia Irazú Hernández Farías, Rafael Guzmán Cabrera, Teodoro Cordova Fraga, José Zacarías Huamaní Luna, Jose Francisco Gomez Aguilar. Modification of the Marching Cubes Algorithm to Obtain a 3D Representation of a Planar Image. Programming and Computer Software. 2021; 47 (3):215-223.

Chicago/Turabian Style

Delia Irazú Hernández Farías; Rafael Guzmán Cabrera; Teodoro Cordova Fraga; José Zacarías Huamaní Luna; Jose Francisco Gomez Aguilar. 2021. "Modification of the Marching Cubes Algorithm to Obtain a 3D Representation of a Planar Image." Programming and Computer Software 47, no. 3: 215-223.

Journal article
Published: 21 April 2021 in Fractals
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ACS Style

Hasib Khan; Thabet Abdeljawad; J. F. Gomez-Aguilar; Haleh Tajadodi; Aziz Khan. Fractional order Volterra integro-differential equation with Mittag-Leffler kernel. Fractals 2021, 1 .

AMA Style

Hasib Khan, Thabet Abdeljawad, J. F. Gomez-Aguilar, Haleh Tajadodi, Aziz Khan. Fractional order Volterra integro-differential equation with Mittag-Leffler kernel. Fractals. 2021; ():1.

Chicago/Turabian Style

Hasib Khan; Thabet Abdeljawad; J. F. Gomez-Aguilar; Haleh Tajadodi; Aziz Khan. 2021. "Fractional order Volterra integro-differential equation with Mittag-Leffler kernel." Fractals , no. : 1.

Journal article
Published: 21 April 2021 in Fractals
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ACS Style

Pallavi Bedi; Anoop Kumar; Thabet Abdeljawad; Aziz Khan; J. F. Gomez-Aguilar. Mild Solutions of Coupled Hybrid Fractional Order System with Caputo-Hadamard Derivatives. Fractals 2021, 1 .

AMA Style

Pallavi Bedi, Anoop Kumar, Thabet Abdeljawad, Aziz Khan, J. F. Gomez-Aguilar. Mild Solutions of Coupled Hybrid Fractional Order System with Caputo-Hadamard Derivatives. Fractals. 2021; ():1.

Chicago/Turabian Style

Pallavi Bedi; Anoop Kumar; Thabet Abdeljawad; Aziz Khan; J. F. Gomez-Aguilar. 2021. "Mild Solutions of Coupled Hybrid Fractional Order System with Caputo-Hadamard Derivatives." Fractals , no. : 1.

Journal article
Published: 20 April 2021 in Mathematics and Computers in Simulation
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In the investigations presented here, an efficient computing approach is applied to solve Human Immunodeficiency Virus (HIV) infection spread. This approach involves CD4+ T-cells by feed-forward artificial neural networks (FF-ANNs) trained with particle swarm optimization (PSO) and interior point method (IPM), i.e., FF-ANN-PSO-IPM. In the proposed solver FF-ANN-PSO-IPM, the FF-ANN models of differential equations are used to develop the fitness functions for an infection model of T-cells. The training of networks through minimization problem are proficiently conducted by integrated heuristic capability of PSO-IPM. The reliability, stability and exactness of the proposed FF-ANN-PSO-IPM are established through comparison with outcomes of standard numerical procedure with Adams method for both single and multiple autonomous trials with precision of order 4 to 8 decimal places of accuracy. The statistical measures are effectively used to validate the outcomes of the proposed FF-ANN-PSO-IPM.

ACS Style

Muhammad Umar; Zulqurnain Sabir; Muhammad Asif Zahoor Raja; J.F. Gómez Aguilar; Fazli Amin; Muhammad Shoaib. Neuro-swarm intelligent computing paradigm for nonlinear HIV infection model with CD4+ T-cells. Mathematics and Computers in Simulation 2021, 188, 241 -253.

AMA Style

Muhammad Umar, Zulqurnain Sabir, Muhammad Asif Zahoor Raja, J.F. Gómez Aguilar, Fazli Amin, Muhammad Shoaib. Neuro-swarm intelligent computing paradigm for nonlinear HIV infection model with CD4+ T-cells. Mathematics and Computers in Simulation. 2021; 188 ():241-253.

Chicago/Turabian Style

Muhammad Umar; Zulqurnain Sabir; Muhammad Asif Zahoor Raja; J.F. Gómez Aguilar; Fazli Amin; Muhammad Shoaib. 2021. "Neuro-swarm intelligent computing paradigm for nonlinear HIV infection model with CD4+ T-cells." Mathematics and Computers in Simulation 188, no. : 241-253.

Article
Published: 25 March 2021 in Optical and Quantum Electronics
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The Drude model has captured minds of many researchers in the past decades because this model is able to explain the transport properties of electrons in materials more precisely metals. This model is an application of kinetic theory that accepts the microscopic behavior of electrons in a solid may be treated characteristically and looks much like a pinball machine. This model is applied for constantly jittering electrons bouncing and re-bouncing off heavier, relatively immobile positive ions. In this manuscript, we consider the mathematical model using the concept of differential operator with two fractional orders. We employ the Laplace transform, inverse Laplace transform and the convolution theorem with analytical method to derive the exact solution of the new equations of the Drude model. Additionally, the three types of sources namely periodic, exponential and unit step are invoked on Drude model for knowing the hidden phenomena of velocity of electrons.

ACS Style

Kashif Ali Abro; Abdon Atangana; José Francisco Gomez-Aguilar. Role of bi-order Atangana–Aguilar fractional differentiation on Drude model: an analytic study for distinct sources. Optical and Quantum Electronics 2021, 53, 1 -14.

AMA Style

Kashif Ali Abro, Abdon Atangana, José Francisco Gomez-Aguilar. Role of bi-order Atangana–Aguilar fractional differentiation on Drude model: an analytic study for distinct sources. Optical and Quantum Electronics. 2021; 53 (4):1-14.

Chicago/Turabian Style

Kashif Ali Abro; Abdon Atangana; José Francisco Gomez-Aguilar. 2021. "Role of bi-order Atangana–Aguilar fractional differentiation on Drude model: an analytic study for distinct sources." Optical and Quantum Electronics 53, no. 4: 1-14.

Journal article
Published: 23 March 2021 in Advances in Difference Equations
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This paper is about to formulate a design of predator–prey model with constant and time fractional variable order. The predator and prey act as agents in an ecosystem in this simulation. We focus on a time fractional order Atangana–Baleanu operator in the sense of Liouville–Caputo. Due to the nonlocality of the method, the predator–prey model is generated by using another FO derivative developed as a kernel based on the generalized Mittag-Leffler function. Two fractional-order systems are assumed, with and without delay. For the numerical solution of the models, we not only employ the Adams–Bashforth–Moulton method but also explore the existence and uniqueness of these schemes. We use the fixed point theorem which is useful in describing the existence of a new approach with a particular set of solutions. For the illustration, several numerical examples are added to the paper to show the effectiveness of the numerical method.

ACS Style

Aziz Khan; Hashim M. Alshehri; J. F. Gómez-Aguilar; Zareen A. Khan; G. Fernández-Anaya. A predator–prey model involving variable-order fractional differential equations with Mittag-Leffler kernel. Advances in Difference Equations 2021, 2021, 1 -18.

AMA Style

Aziz Khan, Hashim M. Alshehri, J. F. Gómez-Aguilar, Zareen A. Khan, G. Fernández-Anaya. A predator–prey model involving variable-order fractional differential equations with Mittag-Leffler kernel. Advances in Difference Equations. 2021; 2021 (1):1-18.

Chicago/Turabian Style

Aziz Khan; Hashim M. Alshehri; J. F. Gómez-Aguilar; Zareen A. Khan; G. Fernández-Anaya. 2021. "A predator–prey model involving variable-order fractional differential equations with Mittag-Leffler kernel." Advances in Difference Equations 2021, no. 1: 1-18.

Special issue paper
Published: 09 March 2021 in Mathematical Methods in the Applied Sciences
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We present a novel master‐slave fractional synchronization in chaotic systems by using fractional derivatives with nonlocal and nonsingular kernel. The master system is the fractional‐order chaotic system, and then, we designed a fractional‐order high gain observer, which is the slave system, based on the chaotic system model to achieve the synchronization. We used three different oscillator systems, a novel Chen‐Burke‐Shaw chaotic attractor, a novel fractional‐order chaotic system, and the fractional‐order model of a simple autonomous Jerk circuit. Our research followed to test the performance of the fractional synchronization. We use two performance indices, the integral of the square error (ISE) and the integral of the square error multiplied by time (ITSE). We showed that by using the fractional‐order approach, we can reduce the values on the ISE and ITSE indices; hence, we guaranteed a full synchronization between the master and slave system. Our analysis shows that when using fractional derivatives with variable order, the ISE and ITSE indices have a lower value than when using the classical derivatives. We used the definition of Atangana‐Baleanu‐Caputo and Liouville‐Caputo derivatives for the three examples mentioned in this work. We numerically solved the equations using the Adams method. Our results show that when using the fractional‐order approach, the ISE and ITSE indices are lower than the integer‐order case.

ACS Style

A. Coronel‐Escamilla; J.F. Gómez‐Aguilar; J. Torres‐Jiménez; A.A. Mousa; S.K. Elagan. Fractional synchronization involving fractional derivatives with nonsingular kernels: Application to chaotic systems. Mathematical Methods in the Applied Sciences 2021, 1 .

AMA Style

A. Coronel‐Escamilla, J.F. Gómez‐Aguilar, J. Torres‐Jiménez, A.A. Mousa, S.K. Elagan. Fractional synchronization involving fractional derivatives with nonsingular kernels: Application to chaotic systems. Mathematical Methods in the Applied Sciences. 2021; ():1.

Chicago/Turabian Style

A. Coronel‐Escamilla; J.F. Gómez‐Aguilar; J. Torres‐Jiménez; A.A. Mousa; S.K. Elagan. 2021. "Fractional synchronization involving fractional derivatives with nonsingular kernels: Application to chaotic systems." Mathematical Methods in the Applied Sciences , no. : 1.