The stability analysis and numerical simulation based on Sinc Legendre collocation method for solving a fractional epidemiological model of the Ebola virus

Abstract

In this paper, we use an efficient numerical method based on Sinc Legendre collocation method for numerically solving fractional model in the caputo sense of the Ebola virus. Fractional derivative is used in the Caputo sense. The Sinc Legendre collocation method are applied to reduce the solution of proposed fractional epidemiological model to the solution of a system of non-linear algebraic equations. Unknown coefficients are obtained by solving final system of non-linear equations by using the Newton–Raphson method. Also, the sinc functions, their properties and Legendre polynomials for our latter expansion are introduced. From Legendre polynomials to approximate the fractional derivatives of sinc functions are used. The proposed numerical method can provide highly accurate approximate solutions by converting the given model under propose to a model of non-linear algebraic equations which is technically easier for doing. The existence, uniqueness solution and Ulam–Hyers​ stability of the proposed method are widely investigated. Finally, some numerical examples are illustrated to show the accuracy, reliability and efficiency of the proposed method. All computations in this paper to solve Ebola virus model are done by applying the Matlab(2020b) software.