Application to Fractional Differential Transformation Method for Solving Fractional SIRC Model and Influenza A

Abstract

In this paper, fractional differential transformation method (FDTM) is performed to give approximate and analytical solutions of nonlinear system of fractional differential equations (FDEs) such as a model for fractional SIRC associated with the evolution of influenza A disease in human population. The fractional derivatives are described in the Caputo sense. Special attention is given to present the local stability of the proposed model. The proposed method introduces a promising tool for solving many nonlinear FDEs. The numerical solutions obtained from the proposed method indicate that the approach is easy to implement and accurate when applied to systems of FDEs. We compared our numerical solutions with those numerical solutions using fourth-order Runge-Kutta method and Chebyshev spectral method. Some figures are presented to show the reliability and the simplicity of the methods.