In this work,we use a Predictor–Corrector method to implement and derive an iterative solution of an existing Tuberculosis(TB)model with two fractional derivatives,namely,Caputo–Fabrizio fractional derivative and th...In this work,we use a Predictor–Corrector method to implement and derive an iterative solution of an existing Tuberculosis(TB)model with two fractional derivatives,namely,Caputo–Fabrizio fractional derivative and the new generalized Caputo fractional derivative.We begin by recalling some existing results such as the basic reproduction number R0 and the equilibrium points of the model.Then,we study the global asymptotic stability of disease-free equilibrium of the fractional models.We also prove,for each fractional model,the existence and uniqueness of solutions.An iterative solution of the two models is computed using the Predictor–Corrector method.Using realistic parameter values,we perform numerical simulations for different values of the fractional order.Simulation results permit to conclude that the new generalized Caputo fractional derivative provides a more realistic analysis than the Caputo–Fabrizio fractional derivative and the classical integer-order TB model.展开更多
This paper proposes fractional-order systems for Hopfield Neural Network(HNN).The so-called Predictor Corrector Adams Bashforth Moulton Method(PCABMM)has been implemented for solving such systems.Graphical comparisons...This paper proposes fractional-order systems for Hopfield Neural Network(HNN).The so-called Predictor Corrector Adams Bashforth Moulton Method(PCABMM)has been implemented for solving such systems.Graphical comparisons between the PCABMM and the Runge-Kutla Method(RKM)solutions for the classical HNN reveal that the proposed technique is one of the powerful tools for handling these systems.To determine all Lyapunov exponents for them,the Benettin-Wolf algorithm has been involved in the PCABMM.leased on such algorithm,the Lyapunov exponents as a function of a given parameter and as another function of the fractional-order have been described,the intermittent chaos for these systems has been explored.A new result related to the Mittag-Leffler stability of some nonlinear Fractional-order Hopfield Neural Network(FoHNN)systems has been shown.Besides,the description and the dynamic analysis of those phenomena have been discussed and verified theoretically and numerically via illustrating the phase portraits and the Lyapunov exponents'diagrams.展开更多
文摘In this work,we use a Predictor–Corrector method to implement and derive an iterative solution of an existing Tuberculosis(TB)model with two fractional derivatives,namely,Caputo–Fabrizio fractional derivative and the new generalized Caputo fractional derivative.We begin by recalling some existing results such as the basic reproduction number R0 and the equilibrium points of the model.Then,we study the global asymptotic stability of disease-free equilibrium of the fractional models.We also prove,for each fractional model,the existence and uniqueness of solutions.An iterative solution of the two models is computed using the Predictor–Corrector method.Using realistic parameter values,we perform numerical simulations for different values of the fractional order.Simulation results permit to conclude that the new generalized Caputo fractional derivative provides a more realistic analysis than the Caputo–Fabrizio fractional derivative and the classical integer-order TB model.
基金supporting this work by the University Ajman Grant:2Q20-COVID-19-08.
文摘This paper proposes fractional-order systems for Hopfield Neural Network(HNN).The so-called Predictor Corrector Adams Bashforth Moulton Method(PCABMM)has been implemented for solving such systems.Graphical comparisons between the PCABMM and the Runge-Kutla Method(RKM)solutions for the classical HNN reveal that the proposed technique is one of the powerful tools for handling these systems.To determine all Lyapunov exponents for them,the Benettin-Wolf algorithm has been involved in the PCABMM.leased on such algorithm,the Lyapunov exponents as a function of a given parameter and as another function of the fractional-order have been described,the intermittent chaos for these systems has been explored.A new result related to the Mittag-Leffler stability of some nonlinear Fractional-order Hopfield Neural Network(FoHNN)systems has been shown.Besides,the description and the dynamic analysis of those phenomena have been discussed and verified theoretically and numerically via illustrating the phase portraits and the Lyapunov exponents'diagrams.
