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In recent years, complex-valued fuzzy metric spaces (in short CVFMS) were introduced by Shukla et al. (Fixed Point Theory 32 (2018)). This setting is a valuable extension of fuzzy metric spaces with the complex grade of membership function. They also established fixed-point results under contractive condition in the aforementioned spaces and generalized some essential existence results in fixed-point theory. The purpose of this manuscript is to derive some fixed-point results for multivalued mappings enjoying the least upper bound property in CVFMS. Furthermore, we studied the existence theorem for a unique solution to the Fuzzy fractional Volterra–Fredholm integro-differential equations (FCFVFIDEs) as an application to our derived result involving the Caputo derivative.
Humaira Humaira; Muhammad Sarwar; Thabet Abdeljawad; Nabil Mlaiki. Fixed Point Results via Least Upper Bound Property and Its Applications to Fuzzy Caputo Fractional Volterra–Fredholm Integro-Differential Equations. Mathematics 2021, 9, 1969 .
AMA StyleHumaira Humaira, Muhammad Sarwar, Thabet Abdeljawad, Nabil Mlaiki. Fixed Point Results via Least Upper Bound Property and Its Applications to Fuzzy Caputo Fractional Volterra–Fredholm Integro-Differential Equations. Mathematics. 2021; 9 (16):1969.
Chicago/Turabian StyleHumaira Humaira; Muhammad Sarwar; Thabet Abdeljawad; Nabil Mlaiki. 2021. "Fixed Point Results via Least Upper Bound Property and Its Applications to Fuzzy Caputo Fractional Volterra–Fredholm Integro-Differential Equations." Mathematics 9, no. 16: 1969.
In this article, we presented a nonlinear time-fractional mathematical model of the Ebola Virus in order to understand the outbreak of this epidemic disease. Ebola virus is a highly contagious disease that can be spread in the population depending upon the number of individuals and their dynamics in the community. The Caputo and Atangana Baleanu fractional derivative operators are employed to get the solution of the system of fractional differential equations. The qualitative analysis has been made for the fractional-order model. Fixed-point theorem and an iterative schemes are used to get the existence and uniqueness. The actual behavior of the time-fractional model has been obtained by employing Laplace Adomian Decomposition technique. Finally, numerical results have been established for the system of fractional differential equations with simulations to demonstrate the impacts of the fractional-order parameters on the proposed system to achieve the theoretical outcomes and a comparison has been made with the Caputo for better analysis.
Muhammad Farman; Ali Akgül; Thabet Abdeljawad; Parvaiz Ahmad Naik; Nabila Bukhari; Aqeel Ahmad. Modeling and analysis of fractional order Ebola virus model with Mittag-Leffler kernel. Alexandria Engineering Journal 2021, 1 .
AMA StyleMuhammad Farman, Ali Akgül, Thabet Abdeljawad, Parvaiz Ahmad Naik, Nabila Bukhari, Aqeel Ahmad. Modeling and analysis of fractional order Ebola virus model with Mittag-Leffler kernel. Alexandria Engineering Journal. 2021; ():1.
Chicago/Turabian StyleMuhammad Farman; Ali Akgül; Thabet Abdeljawad; Parvaiz Ahmad Naik; Nabila Bukhari; Aqeel Ahmad. 2021. "Modeling and analysis of fractional order Ebola virus model with Mittag-Leffler kernel." Alexandria Engineering Journal , no. : 1.
This manuscript is devoted to consider population dynamical model of non-integer order to investigate the recent pandemic Covid-19 named as severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) disease. We investigate the proposed model corresponding to different values of largely effected system parameter of immigration for both susceptible and infected populations. The results for qualitative analysis are established with the help of fixed-point theory and non-linear functional analysis. Moreover, semi-analytical results, related to series solution for the considered system are investigated on applying the transform due to Laplace with Adomian polynomial and decomposition techniques. We have also applied the non-standard finite difference scheme (NSFD) for numerical solution. Finally, both the analysis are supported by graphical results at various fractional order. Both the results are comparable with each other and converging quickly at low order. The whole spectrum and the dynamical behavior for each compartment of the proposed model lying between 0 and 1 are simulated via Matlab.
Muhammad Arfan; Ibrahim Mahariq; Kamal Shah; Thabet Abdeljawad; Ghaylen Laouini; Pshtiwan Othman Mohammed. Numerical computations and theoretical investigations of a dynamical system with fractional order derivative. Alexandria Engineering Journal 2021, 1 .
AMA StyleMuhammad Arfan, Ibrahim Mahariq, Kamal Shah, Thabet Abdeljawad, Ghaylen Laouini, Pshtiwan Othman Mohammed. Numerical computations and theoretical investigations of a dynamical system with fractional order derivative. Alexandria Engineering Journal. 2021; ():1.
Chicago/Turabian StyleMuhammad Arfan; Ibrahim Mahariq; Kamal Shah; Thabet Abdeljawad; Ghaylen Laouini; Pshtiwan Othman Mohammed. 2021. "Numerical computations and theoretical investigations of a dynamical system with fractional order derivative." Alexandria Engineering Journal , no. : 1.
In the present article, we investigate the dual slip effect namely the velocity slip and thermal slip conditions on MHD flow past a thin needle. The entropy generation for the incompressible fluids that’s water and acetone that flowing above the thin needle is discussed. The energy dissipating term and the magnetic effect is included in the axial direction. The leading partial differential equations are transformed to ODE by an appropriate similarity transformation and solved using a numerical technique that is the Quasilinearization method. The terms for the rate of entropy generation, the Bejan number, and the irreversibility distribution ratio are discussed. Each dimensionless number is shown with velocity slip and also with the magnetic parameter is presented in graphical form. In the result, we conclude that the entropy generation rate is increasing with the increase in thermal slip parameter also some increasing effect is found as the size of the needle increases
Sohaib Khan; Farhad Ali; Waqar A. Khan; Anees Imtiaz; İlyas Khan; Thabet Abdeljawad. Quasilinearization numerical technique for dual slip MHD Newtonian fluid flow with entropy generation in thermally dissipating flow above a thin needle. Scientific Reports 2021, 11, 1 -13.
AMA StyleSohaib Khan, Farhad Ali, Waqar A. Khan, Anees Imtiaz, İlyas Khan, Thabet Abdeljawad. Quasilinearization numerical technique for dual slip MHD Newtonian fluid flow with entropy generation in thermally dissipating flow above a thin needle. Scientific Reports. 2021; 11 (1):1-13.
Chicago/Turabian StyleSohaib Khan; Farhad Ali; Waqar A. Khan; Anees Imtiaz; İlyas Khan; Thabet Abdeljawad. 2021. "Quasilinearization numerical technique for dual slip MHD Newtonian fluid flow with entropy generation in thermally dissipating flow above a thin needle." Scientific Reports 11, no. 1: 1-13.
In this paper, we study classes of linear and nonlinear multi-term fractional differential equations involving a fractional derivative with generalized Mittag-Leffler kernel. Estimates of fractional derivatives at extreme points are first obtained and then implemented to derive new comparison principles for related linear equations. These comparison principles are used to analyze the solutions of the linear multi-term equations, where norm estimates of solutions, uniqueness and several comparison results are established. For the nonlinear problem, we apply the Banach fixed point theorem to establish the existence of a unique solution.
Mohammed Al-Refai; Abdalla Aljarrah; Thabet Abdeljawad. Analysis of fractional differential equations with fractional derivative of generalized Mittag-Leffler kernel. Advances in Difference Equations 2021, 2021, 1 -10.
AMA StyleMohammed Al-Refai, Abdalla Aljarrah, Thabet Abdeljawad. Analysis of fractional differential equations with fractional derivative of generalized Mittag-Leffler kernel. Advances in Difference Equations. 2021; 2021 (1):1-10.
Chicago/Turabian StyleMohammed Al-Refai; Abdalla Aljarrah; Thabet Abdeljawad. 2021. "Analysis of fractional differential equations with fractional derivative of generalized Mittag-Leffler kernel." Advances in Difference Equations 2021, no. 1: 1-10.
The Prabhakar fractional operator is commonly acclaimed as the queen model of fractional calculus. Our aim in this article is to introduce the notion of the discrete Prabhakar fractional operator with discrete generalized Mittag-Leffler function in the kernel, in the context of discrete fractional calculus. Also, we examine some relationships between our new model with the discrete Atangana–Baleanu fractional model implemented by Abdeljawad. By doing these relationships, we can find a few interesting properties of both, as well as of the original discrete Atangana–Baleanu fractional models and their iterated forms. We can confirm that this is the first paper introducing and studying the discrete Prabhakar fractional operators in the context of discrete fractional calculus.
Pshtiwan Othman Mohammed; Thabet Abdeljawad; Faraidun Kadir Hamasalh. Discrete Prabhakar fractional difference and sum operators. Chaos, Solitons & Fractals 2021, 150, 111182 .
AMA StylePshtiwan Othman Mohammed, Thabet Abdeljawad, Faraidun Kadir Hamasalh. Discrete Prabhakar fractional difference and sum operators. Chaos, Solitons & Fractals. 2021; 150 ():111182.
Chicago/Turabian StylePshtiwan Othman Mohammed; Thabet Abdeljawad; Faraidun Kadir Hamasalh. 2021. "Discrete Prabhakar fractional difference and sum operators." Chaos, Solitons & Fractals 150, no. : 111182.
The task of root-finding of the non-linear equations is perhaps, one of the most complicated problems in applied mathematics especially in a diverse range of engineering applications. The characteristics of the root-finding methods such as convergence rate, performance, efficiency, etc., are directly relied upon the initial guess of the solution to execute the process in most of the systems of non-linear equations. Keeping these facts into mind, based on Taylor’s series expansion, we present some new modifications of Halley, Househölder and Golbabai and Javidi’s methods and then making them second derivative free by applying Taylor’s series. The convergence analysis of the suggested methods is discussed. It is established that the proposed methods possess convergence of orders five and six. Several numerical problems have been tested to demonstrate the validity and applicability of the proposed methods. These test examples also include some real-life problems associated with chemical and civil engineering such as open channel flow problem, the adiabatic flame temperature equation, conversion of nitrogen-hydrogen feed to ammonia and the van der Wall’s equation whose numerical results prove the better performance of the suggested methods as compared to other well-known existing methods of the same kind in the literature. Finally, the dynamics of the presented algorithms in the form of polynomiographs have been shown with the aid of computer program by considering some complex polynomials and compared them with the other well-known iterative algorithms that revealed the convergence speed and other dynamical aspects of the presented methods.
Amir Naseem; M. A. Rehman; Thabet Abdeljawad; Yu-Ming Chu. Novel Iteration Schemes for Computing Zeros of Non-Linear Equations with Engineering Applications and Their Dynamics. IEEE Access 2021, 9, 1 -1.
AMA StyleAmir Naseem, M. A. Rehman, Thabet Abdeljawad, Yu-Ming Chu. Novel Iteration Schemes for Computing Zeros of Non-Linear Equations with Engineering Applications and Their Dynamics. IEEE Access. 2021; 9 ():1-1.
Chicago/Turabian StyleAmir Naseem; M. A. Rehman; Thabet Abdeljawad; Yu-Ming Chu. 2021. "Novel Iteration Schemes for Computing Zeros of Non-Linear Equations with Engineering Applications and Their Dynamics." IEEE Access 9, no. : 1-1.
This study is aimed to investigate the sufficient conditions of the existence of unique solutions and the Ulam–Hyers–Mittag-Leffler (UHML) stability for a tripled system of weighted generalized Caputo fractional derivatives investigated by Jarad et al. (Fractals 28:2040011 2020) in the frame of Chebyshev and Bielecki norms with time delay. The acquired results are obtained by using Banach fixed point theorems and the Picard operator (PO) method. Finally, a pertinent example of the results obtained is demonstrated.
Mohammed A. Almalahi; Satish K. Panchal; Fahd Jarad; Thabet Abdeljawad. Ulam–Hyers–Mittag-Leffler stability for tripled system of weighted fractional operator with TIME delay. Advances in Difference Equations 2021, 2021, 1 -18.
AMA StyleMohammed A. Almalahi, Satish K. Panchal, Fahd Jarad, Thabet Abdeljawad. Ulam–Hyers–Mittag-Leffler stability for tripled system of weighted fractional operator with TIME delay. Advances in Difference Equations. 2021; 2021 (1):1-18.
Chicago/Turabian StyleMohammed A. Almalahi; Satish K. Panchal; Fahd Jarad; Thabet Abdeljawad. 2021. "Ulam–Hyers–Mittag-Leffler stability for tripled system of weighted fractional operator with TIME delay." Advances in Difference Equations 2021, no. 1: 1-18.
This article describes the corona virus spread in a population under certain assumptions with the help of a fractional order mathematical model. The fractional order derivative is the well-known fractal fractional operator. We have given the existence results and numerical simulations with the help of the given data in the literature. Our results show similar behavior as the classical order ones. This characteristic shows the applicability and usefulness of the derivative and our numerical scheme.
Hasib Khan; Razia Begum; Thabet Abdeljawad; M. Motawi Khashan. A numerical and analytical study of SE(Is)(Ih)AR epidemic fractional order COVID-19 model. Advances in Difference Equations 2021, 2021, 1 -31.
AMA StyleHasib Khan, Razia Begum, Thabet Abdeljawad, M. Motawi Khashan. A numerical and analytical study of SE(Is)(Ih)AR epidemic fractional order COVID-19 model. Advances in Difference Equations. 2021; 2021 (1):1-31.
Chicago/Turabian StyleHasib Khan; Razia Begum; Thabet Abdeljawad; M. Motawi Khashan. 2021. "A numerical and analytical study of SE(Is)(Ih)AR epidemic fractional order COVID-19 model." Advances in Difference Equations 2021, no. 1: 1-31.
This manuscripts main objective is to examine the existence of piecewise-continuous mild solution of Atangana-Baleanu fractional Volterra-Fredholm integro-differential inclusions (ABFVFIDI) with non-instantaneous impulses (NII) in Banach space. Based on Martelli’s fixed point theorem and ρ-resolvent operators, we develop the main results. An example is given to support the validation of the theoretical results achieved.
M. Mallika Arjunan; Thabet Abdeljawad; V. Kavitha; Ali Yousef. On a new class of Atangana-Baleanu fractional Volterra-Fredholm integro-differential inclusions with non-instantaneous impulses. Chaos, Solitons & Fractals 2021, 148, 111075 .
AMA StyleM. Mallika Arjunan, Thabet Abdeljawad, V. Kavitha, Ali Yousef. On a new class of Atangana-Baleanu fractional Volterra-Fredholm integro-differential inclusions with non-instantaneous impulses. Chaos, Solitons & Fractals. 2021; 148 ():111075.
Chicago/Turabian StyleM. Mallika Arjunan; Thabet Abdeljawad; V. Kavitha; Ali Yousef. 2021. "On a new class of Atangana-Baleanu fractional Volterra-Fredholm integro-differential inclusions with non-instantaneous impulses." Chaos, Solitons & Fractals 148, no. : 111075.
Monotonicity analysis of delta fractional sums and differences of order
Pshtiwan Mohammed; Thabet Abdeljawad; Faraidun Hamasalh. On Riemann—Liouville and Caputo Fractional Forward Difference Monotonicity Analysis. Mathematics 2021, 9, 1303 .
AMA StylePshtiwan Mohammed, Thabet Abdeljawad, Faraidun Hamasalh. On Riemann—Liouville and Caputo Fractional Forward Difference Monotonicity Analysis. Mathematics. 2021; 9 (11):1303.
Chicago/Turabian StylePshtiwan Mohammed; Thabet Abdeljawad; Faraidun Hamasalh. 2021. "On Riemann—Liouville and Caputo Fractional Forward Difference Monotonicity Analysis." Mathematics 9, no. 11: 1303.
In this article, we established a new version of generalized fractional Hadamard and Fejér–Hadamard type integral inequalities. A fractional integral operator (FIO) with a non-singular function (multi-index Bessel function) as its kernel and monotone increasing functions is utilized to obtain the new version of such fractional inequalities. Our derived results are a generalized form of several proven inequalities already existing in the literature. The proven inequalities are useful for studying the stability and control of corresponding fractional dynamic equations.
Rana Ali; Aiman Mukheimer; Thabet Abdeljawad; Shahid Mubeen; Sabila Ali; Gauhar Rahman; Kottakkaran Nisar. Some New Harmonically Convex Function Type Generalized Fractional Integral Inequalities. Fractal and Fractional 2021, 5, 54 .
AMA StyleRana Ali, Aiman Mukheimer, Thabet Abdeljawad, Shahid Mubeen, Sabila Ali, Gauhar Rahman, Kottakkaran Nisar. Some New Harmonically Convex Function Type Generalized Fractional Integral Inequalities. Fractal and Fractional. 2021; 5 (2):54.
Chicago/Turabian StyleRana Ali; Aiman Mukheimer; Thabet Abdeljawad; Shahid Mubeen; Sabila Ali; Gauhar Rahman; Kottakkaran Nisar. 2021. "Some New Harmonically Convex Function Type Generalized Fractional Integral Inequalities." Fractal and Fractional 5, no. 2: 54.
The purpose of this article is to extend the fractional third order dispersive PDE under singular and non-singular fractional operators via the notion of fuzziness. We investigate the fuzzy dispersive PDE in one and higher dimension under Caputo, Caputo-Fabrizio, and Atangana-Baleanu fractional operators and provide two examples to each derivative. We derive the general algorithm and numerical results in series of the models and test problems with the help of fuzzy Laplace transform. The numerical results confirm that solutions obtained in the fuzzy sense are more generalized than the fractional-order solution. We mention in remarks following each example that we recover the solutions of the fractional-order equations by putting the lower and upper functions of the fuzzy number g̃ equals to 1 in the fuzzy solutions of the proposed dispersive PDEs. We demonstrate the numerical results through 2D and 3D plots for different fractional-order and uncertainty k∈[0,1]. We provide a comparison between Caputo, Caputo-Fabrizio and Atangana-Baleanu fuzzy fractional dispersive PDE. In the end, we give the conclusion of the article and future work.
Shabir Ahmad; Aman Ullah; Ali Akgül; Thabet Abdeljawad. Semi-analytical solutions of the 3 order fuzzy dispersive partial differential equations under fractional operators. Alexandria Engineering Journal 2021, 60, 5861 -5878.
AMA StyleShabir Ahmad, Aman Ullah, Ali Akgül, Thabet Abdeljawad. Semi-analytical solutions of the 3 order fuzzy dispersive partial differential equations under fractional operators. Alexandria Engineering Journal. 2021; 60 (6):5861-5878.
Chicago/Turabian StyleShabir Ahmad; Aman Ullah; Ali Akgül; Thabet Abdeljawad. 2021. "Semi-analytical solutions of the 3 order fuzzy dispersive partial differential equations under fractional operators." Alexandria Engineering Journal 60, no. 6: 5861-5878.
The concept of the neutrosophic hypersoft set (NHSS) is a parameterized family that deals with the subattributes of the parameters and is a proper extension of the neutrosophic soft set to accurately assess the deficiencies, anxiety, and uncertainty in decision-making. Compared with existing research, NHSS can accommodate more uncertainty, which is the most significant technique for describing fuzzy information in the decision-making process. The main objective of the follow-up study is to develop the theory of neutrosophic hypersoft matrix (NHSM). The NHSM is the generalized form of a neutrosophic soft matrix (NSM). Some fundamental operations and score function for NHSMs have been introduced with their desirable properties. Furthermore, we introduce the logical operators such as OR-operator and AND-operator with their fundamental properties in the following research. The necessity and possibility operations for NHSMs have been established. Utilizing the developed score function, a decision-making methodology has been developed to solve the multiattribute decision-making (MADM) problem. To ensure the validity of the proposed approach, a numerical illustration has been described for the selection of competent faculty member. The practicality and effectiveness of the current approach are proved through comparative analysis with the assistance of some existing studies.
Rana Muhammad Zulqarnain; Imran Siddique; Rifaqat Ali; Fahd Jarad; Abdul Samad; Thabet Abdeljawad. Neutrosophic Hypersoft Matrices with Application to Solve Multiattributive Decision-Making Problems. Complexity 2021, 2021, 1 -17.
AMA StyleRana Muhammad Zulqarnain, Imran Siddique, Rifaqat Ali, Fahd Jarad, Abdul Samad, Thabet Abdeljawad. Neutrosophic Hypersoft Matrices with Application to Solve Multiattributive Decision-Making Problems. Complexity. 2021; 2021 ():1-17.
Chicago/Turabian StyleRana Muhammad Zulqarnain; Imran Siddique; Rifaqat Ali; Fahd Jarad; Abdul Samad; Thabet Abdeljawad. 2021. "Neutrosophic Hypersoft Matrices with Application to Solve Multiattributive Decision-Making Problems." Complexity 2021, no. : 1-17.
Correlation coefficients are used to tackle many issues that include indistinct as well as blurred information excluding is not able to deal with the general fuzziness along with obscurity of the problems that have various information. The correlation coefficient (CC) between two variables plays an important role in statistics. Likewise, the accuracy of relevance assessment depends on the information in a set of discourses. The data collected for numerous statistical studies is full of exceptions. The concept of the neutrosophic hypersoft set (NHSS) is a parameterized family that deals with the subattributes of the parameters and is a proper extension of the neutrosophic soft set to accurately assess the deficiencies, anxiety, and uncertainty in decision-making. Compared with existing research, NHSS can accommodate more uncertainty, which is the most significant technique for describing fuzzy information in the decision-making process. The core objective of follow-up research is to develop the concept and characteristics of CC and the weighted correlation coefficient (WCC) of NHSS. We also introduced some aggregation operators in the considered environment, which can help us establish a prioritization technique for order preference by similarity to the ideal solution (TOPSIS) based on CC and WCC under NHSS. A decision-making strategy is established to solve multicriteria group decision-making (MCGDM) problems utilizing developed methodology. Moreover, the proposed method is utilized for the selection of an effective hand sanitizer during the COVID-19 pandemic to ensure the validity of the proposed approach. The practicality, effectivity, and flexibility of the current approach are proved through comparative analysis with the assistance of some existing studies.
Abdul Samad; Rana Muhammad Zulqarnain; Emre Sermutlu; Rifaqat Ali; Imran Siddique; Fahd Jarad; Thabet Abdeljawad. Selection of an Effective Hand Sanitizer to Reduce COVID-19 Effects and Extension of TOPSIS Technique Based on Correlation Coefficient under Neutrosophic Hypersoft Set. Complexity 2021, 2021, 1 -22.
AMA StyleAbdul Samad, Rana Muhammad Zulqarnain, Emre Sermutlu, Rifaqat Ali, Imran Siddique, Fahd Jarad, Thabet Abdeljawad. Selection of an Effective Hand Sanitizer to Reduce COVID-19 Effects and Extension of TOPSIS Technique Based on Correlation Coefficient under Neutrosophic Hypersoft Set. Complexity. 2021; 2021 ():1-22.
Chicago/Turabian StyleAbdul Samad; Rana Muhammad Zulqarnain; Emre Sermutlu; Rifaqat Ali; Imran Siddique; Fahd Jarad; Thabet Abdeljawad. 2021. "Selection of an Effective Hand Sanitizer to Reduce COVID-19 Effects and Extension of TOPSIS Technique Based on Correlation Coefficient under Neutrosophic Hypersoft Set." Complexity 2021, no. : 1-22.
An important area in the field of applied and pure mathematics is the integral inequality. As it is known, inequalities aim to develop different mathematical methods. Nowadays, we need to seek accurate inequalities for proving the existence and uniqueness of the mathematical methods. The concept of convexity plays a strong role in the field of inequalities due to the behavior of its definition and its properties. Furthermore, there is a strong correlation between convexity and symmetry concepts. Whichever one we work on, we can apply it to the other one due the strong correlation produced between them, especially in the last few years. In this study, by using a new identity, we establish some new fractional weighted Ostrowski-type inequalities for differentiable quasi-convex functions. Further, further results for functions with a bounded first derivative are given. Finally, in order to illustrate the efficiency of our main results, some applications to special means are obtain. The obtained results generalize and refine certain known results.
Artion Kashuri; Badreddine Meftah; Pshtiwan Mohammed; Alina Lupaş; Bahaaeldin Abdalla; Y. Hamed; Thabet Abdeljawad. Fractional Weighted Ostrowski-Type Inequalities and Their Applications. Symmetry 2021, 13, 968 .
AMA StyleArtion Kashuri, Badreddine Meftah, Pshtiwan Mohammed, Alina Lupaş, Bahaaeldin Abdalla, Y. Hamed, Thabet Abdeljawad. Fractional Weighted Ostrowski-Type Inequalities and Their Applications. Symmetry. 2021; 13 (6):968.
Chicago/Turabian StyleArtion Kashuri; Badreddine Meftah; Pshtiwan Mohammed; Alina Lupaş; Bahaaeldin Abdalla; Y. Hamed; Thabet Abdeljawad. 2021. "Fractional Weighted Ostrowski-Type Inequalities and Their Applications." Symmetry 13, no. 6: 968.
The novel coronavirus infectious disease (or COVID-19) almost spread widely around the world and causes a huge panic in the human population. To explore the complex dynamics of this novel infection, several mathematical epidemic models have been adopted and simulated using the statistical data of COVID-19 in various regions. In this paper, we present a new nonlinear fractional order model in the Caputo sense to analyze and simulate the dynamics of this viral disease with a case study of Algeria. Initially, after the model formulation, we utilize the well-known least square approach to estimate the model parameters from the reported COVID-19 cases in Algeria for a selected period of time. We perform the existence and uniqueness of the model solution which are proved via the Picard-Lindelöf method. We further compute the basic reproduction numbers and equilibrium points, then we explore the local and global stability of both the disease-free equilibrium point and the endemic equilibrium point. Finally, numerical results and graphical simulation are given to demonstrate the impact of various model parameters and fractional order on the disease dynamics and control.
Yacine El Hadj Moussa; Ahmed Boudaoui; Saif Ullah; Fatma Bozkurt; Thabet Abdeljawad; Manar A. Alqudah. Stability analysis and simulation of the novel Corornavirus mathematical model via the Caputo fractional-order derivative: A case study of Algeria. Results in Physics 2021, 26, 104324 -104324.
AMA StyleYacine El Hadj Moussa, Ahmed Boudaoui, Saif Ullah, Fatma Bozkurt, Thabet Abdeljawad, Manar A. Alqudah. Stability analysis and simulation of the novel Corornavirus mathematical model via the Caputo fractional-order derivative: A case study of Algeria. Results in Physics. 2021; 26 ():104324-104324.
Chicago/Turabian StyleYacine El Hadj Moussa; Ahmed Boudaoui; Saif Ullah; Fatma Bozkurt; Thabet Abdeljawad; Manar A. Alqudah. 2021. "Stability analysis and simulation of the novel Corornavirus mathematical model via the Caputo fractional-order derivative: A case study of Algeria." Results in Physics 26, no. : 104324-104324.
At first, we recall the q-operators in the context of q-calculus and by examining these operators we will introduce new definitions of the partial q-operators. Then, we investigate some new refinements inequalities of Hermite–Hadamard ( $H-H$ H − H ) type on the coordinated convex functions involving the new defined partial q-operators. From our main results, we establish several specific inequalities and we point out the existing results which had already been obtained in the literature.
Manar A. Alqudah; Artion Kashuri; Pshtiwan Othman Mohammed; Thabet Abdeljawad; Muhammad Raees; Matloob Anwar; Y. S. Hamed. Hermite–Hadamard integral inequalities on coordinated convex functions in quantum calculus. Advances in Difference Equations 2021, 2021, 1 -29.
AMA StyleManar A. Alqudah, Artion Kashuri, Pshtiwan Othman Mohammed, Thabet Abdeljawad, Muhammad Raees, Matloob Anwar, Y. S. Hamed. Hermite–Hadamard integral inequalities on coordinated convex functions in quantum calculus. Advances in Difference Equations. 2021; 2021 (1):1-29.
Chicago/Turabian StyleManar A. Alqudah; Artion Kashuri; Pshtiwan Othman Mohammed; Thabet Abdeljawad; Muhammad Raees; Matloob Anwar; Y. S. Hamed. 2021. "Hermite–Hadamard integral inequalities on coordinated convex functions in quantum calculus." Advances in Difference Equations 2021, no. 1: 1-29.
The 3D Carreau fluid flow through a porous and stretching (shrinking) sheet is examined analytically by taking into account the effects of mass transfer, thermal radiation, and Hall current. The model equations, which consist of coupled partial differential equations (PDEs), are simplified to ordinary differential equations (ODEs) through appropriate similarity relations. The analytical procedure of HAM (homotopy analysis method) is employed to solve the coupled set of ODEs. The functional dependence of the hydromagnetic 3D Carreau fluid flow on the pertinent parameters are displayed through various plots. It is found that the x-component of velocity gradient (
Shahid Khan; Mahmoud Selim; Aziz Khan; Asad Ullah; Thabet Abdeljawad; Ikramullah; Muhammad Ayaz; Wali Mashwani. On the Analysis of the Non-Newtonian Fluid Flow Past a Stretching/Shrinking Permeable Surface with Heat and Mass Transfer. Coatings 2021, 11, 566 .
AMA StyleShahid Khan, Mahmoud Selim, Aziz Khan, Asad Ullah, Thabet Abdeljawad, Ikramullah, Muhammad Ayaz, Wali Mashwani. On the Analysis of the Non-Newtonian Fluid Flow Past a Stretching/Shrinking Permeable Surface with Heat and Mass Transfer. Coatings. 2021; 11 (5):566.
Chicago/Turabian StyleShahid Khan; Mahmoud Selim; Aziz Khan; Asad Ullah; Thabet Abdeljawad; Ikramullah; Muhammad Ayaz; Wali Mashwani. 2021. "On the Analysis of the Non-Newtonian Fluid Flow Past a Stretching/Shrinking Permeable Surface with Heat and Mass Transfer." Coatings 11, no. 5: 566.
In this article, we debate the existence of solutions for a nonlinear Hilfer fractional differential inclusion with nonlocal Erdélyi–Kober fractional integral boundary conditions (FIBC). Both cases of convex- and nonconvex-valued right-hand side are considered. Our obtained results are new in the framework of Hilfer fractional derivative and Erdélyi–Kober fractional integral with FIBC via the fixed point theorems (FPTs) for a set-valued analysis. Some pertinent examples demonstrating the effectiveness of the theoretical results are presented.
Adel Lachouri; Mohammed S. Abdo; Abdelouaheb Ardjouni; Bahaaeldin Abdalla; Thabet Abdeljawad. Hilfer fractional differential inclusions with Erdélyi–Kober fractional integral boundary condition. Advances in Difference Equations 2021, 2021, 1 -17.
AMA StyleAdel Lachouri, Mohammed S. Abdo, Abdelouaheb Ardjouni, Bahaaeldin Abdalla, Thabet Abdeljawad. Hilfer fractional differential inclusions with Erdélyi–Kober fractional integral boundary condition. Advances in Difference Equations. 2021; 2021 (1):1-17.
Chicago/Turabian StyleAdel Lachouri; Mohammed S. Abdo; Abdelouaheb Ardjouni; Bahaaeldin Abdalla; Thabet Abdeljawad. 2021. "Hilfer fractional differential inclusions with Erdélyi–Kober fractional integral boundary condition." Advances in Difference Equations 2021, no. 1: 1-17.