We consider a SEAIR epidemic model with Atangana–Baleanu fractional-order derivative. We approximate the solution of the model using the numerical scheme developed by Toufic and Atangana. The numerical simulation corresponding to several fractional orders shows that, as the fractional order reduces from 1, the spread of the endemic grows slower. Optimal control analysis and simulation show that the control strategy designed is operative in reducing the number of cases in different compartments. Moreover, simulating the optimal profile revealed that reducing the fractional-order from 1 leads to the need for quick starting of the application of the designed control strategy at the maximum possible level and maintaining it for the majority of the period of the pandemic.

This paper is devoted to generalizing the standard system of Navier boundary value problems to a fractional system of coupled sequential Navier boundary value problems by using terms of the Caputo derivatives. In other words, for the first time, we design a multi-term fractional coupled system of Navier equations under the fractional boundary conditions. The existence theory is studied regarding solutions of the given coupled sequential Navier boundary problems via the Krasnoselskii’s fixed-point theorem on two nonlinear operators. Moreover, the Banach contraction principle is applied to investigate the uniqueness of solution. We then focus on the Hyers–Ulam-type stability of its solution. Furthermore, the approximate solutions of the proposed coupled fractional sequential Navier system are obtained via the generalized differential transform method. Lastly, the results of this research are supported by giving simulated examples.

Few studies have investigated the existence and uniqueness of solutions for fractional differential equations on star graphs until now. The published papers on the topic are based on the assumption of existence of one junction node and some boundary nodes as the origin on a star graph. These structures are special cases and do not cover more general non-star graph structures. In this paper, we state a labeling method for graph vertices, and then we prove the existence results for solutions to a new family of fractional boundary value problems (FBVPs) on the methylpropane graph. We design the chemical compound of the methylpropane graph with vertices specified by 0 or 1, and on every edge of the graph, we consider fractional differential equations. We prove the existence of solutions for the proposed FBVPs by means of the Krasnoselskii’s and Scheafer’s fixed point theorems, and further, we study the Ulam–Hyers type stability for the given multi-dimensional system. Finally, we provide an illustrative example to examine our results.

The Lorenz-Stenflo mathematical model describes a complex dynamical behavior related to atmospheric acoustic-gravity waves. In this study, qualitative analysis of the four-dimensional hyperchaotic Lorenz-Stenflo system via the Caputo fractional derivative is implemented. By using the Matignon stability criterion, the local stability analysis of the system showed that all the equilibrium points of the system are locally unstable. Calculation of the Lyapunov exponents along with the relevant bifurcation diagrams with respect to different fractional orders exposed the hyperchaotic dynamical behavior for the system. Bifurcation diagrams for all the four parameters in the system also showed the hyperchaotic nature of the Lorenz-Stenflo system. Different phase attractors of the system corresponding to different fractional derivatives and parameters are presented to specify the dynamical nature of the system. The Lorenz-Stenflo system showed sensitivity to initial conditions. The master and slave systems showed a strong correlation among themselves, as verified by graphs of time series solutions of the two systems.

Drugs have always been one of the most important concerns of families and government officials at all times, and they have caused irreparable damage to the health of young people. Given the importance of this great challenge, this article discusses a non-symmetric fractal-fractional order ice-smoking mathematical model for the existence results, numerical results, and stability analysis. For the existence of the solution of the given ice-smoking model, successive iterative sequences are defined. The uniqueness of the solution Hyers–Ulam (HU) stability is established with the help of the existing definitions and theorems in functional analysis. By the utilization of two-step Lagrange polynomials, we provide numerical solutions and provide a comparative numerical analysis for different values of the fractional order and fractal order. The numerical simulations show the applicability of the scheme and future prediction and the effects of fractal-fractional orders simultaneously.

Malaria is a complex disease with many factors influencing the transmission dynamics, including age. This research analyzes the transmission dynamics of malaria by developing an age-structured mathematical model using the classical integer order and Atangana–Baleanu–Caputo fractional operators. The analysis of the model focused on several important aspects. The existence and uniqueness of solutions of fractional order were explored based on some fixed-point theorems,such as Banach and Krasnoselski. The Positivity and boundedness of the solutions were also investigated. Furthermore, through mathematical analysis techniques, we analyzed different types of stability results, and the results showed that the disease-free equilibrium point of the model is proved to be both locally and globally asymptotically stable if the basic reproduction number is less than one, whereas the endemic equilibrium point of the model is both locally and globally asymptotically stable if the basic reproduction number is greater than one. The findings from the sensitivity analysis revealed that the most sensitive parameters, essential for controlling or eliminating malaria are mosquito biting rate, density-dependent natural mortality rate, clinical recovery rate, and recruitment rate for mosquitoes. Numerical simulations are also performed to examine the behavior of the model for different values of the fractional-order alpha,and the result revealed that as the value α reduces from 1, the spread of the endemic grows slower. By incorporating these findings, this research helps to clarify the dynamics of malaria and provides information on how to create efficient control measures.