In this paper we refer to equations of motion for the single Stokes pulse from the nonlinear optics, called the Stokes pulse system. A fractional-order model with Caputo derivative associated to Stokes pulse system (c...In this paper we refer to equations of motion for the single Stokes pulse from the nonlinear optics, called the Stokes pulse system. A fractional-order model with Caputo derivative associated to Stokes pulse system (called the fractional Stokes pulse system) is proposed. The existence and uniqueness of solution of initial value problem for this fractional system are proved. The dynamic behavior for a special fractional Stokes pulse system is investigated, including: the fractional stability, the stabilization problem using suitable linear controls and the numerical integration based on fractional Euler method.展开更多
In this paper,we study two fractional models in the Caputo–Fabrizio sense and Atangana–Baleanu sense,in which the effects of malaria infection on mosquito biting behavior and attractiveness of humans are considered....In this paper,we study two fractional models in the Caputo–Fabrizio sense and Atangana–Baleanu sense,in which the effects of malaria infection on mosquito biting behavior and attractiveness of humans are considered.Using Lyapunov theory,we prove the global asymptotic stability of the unique endemic equilibrium of the integer-order model,and the fractional models,whenever the basic reproduction number R0 is greater than one.By using fixed point theory,we prove existence,and conditions of the uniqueness of solutions,as well as the stability and convergence of numerical schemes.Numerical simulations for both models,using fractional Euler method and Adams–Bashforth method,respectively,are provided to confirm the effectiveness of used approximation methods for different values of the fractional-orderγ.展开更多
文摘In this paper we refer to equations of motion for the single Stokes pulse from the nonlinear optics, called the Stokes pulse system. A fractional-order model with Caputo derivative associated to Stokes pulse system (called the fractional Stokes pulse system) is proposed. The existence and uniqueness of solution of initial value problem for this fractional system are proved. The dynamic behavior for a special fractional Stokes pulse system is investigated, including: the fractional stability, the stabilization problem using suitable linear controls and the numerical integration based on fractional Euler method.
文摘In this paper,we study two fractional models in the Caputo–Fabrizio sense and Atangana–Baleanu sense,in which the effects of malaria infection on mosquito biting behavior and attractiveness of humans are considered.Using Lyapunov theory,we prove the global asymptotic stability of the unique endemic equilibrium of the integer-order model,and the fractional models,whenever the basic reproduction number R0 is greater than one.By using fixed point theory,we prove existence,and conditions of the uniqueness of solutions,as well as the stability and convergence of numerical schemes.Numerical simulations for both models,using fractional Euler method and Adams–Bashforth method,respectively,are provided to confirm the effectiveness of used approximation methods for different values of the fractional-orderγ.
