An Operational Matrix of Hermite Polynomials for Solving Nonlinear Fractional Dierential Equations

In this paper, an effective technique known as the operational matrix method is utilised to solve nonlinear form of fractional dierential equations (FDEs). An explicit effort is placed on the derivation of Hermite polynomials operational matrix with the Caputo sense. The main motivation behind this work is to convert a nonlinear type of FDE into a set of algebraic equations with the consideration of initial conditions. The problem is therefore simplied by these equations to be solved with the proposed method. In order to conrm the effectiveness of the proposed approach, numerical and analytical solutions for a number of nonlinear FDEs are presented. Due to the high simplicity of the proposed approach in practice, it can be comfortably implemented in various aspects of applied science domain.