Hermite Operational Matrix for Solving Fractional Differential Equations

Abstract

This paper aims to solve the fractional differential equations (FDEs) with operational matrix method by Hermite polynomials in the sense of Caputo derivative. For this purpose, we attempt to re-define the FDEs with a set of algebraic equations with initial conditions which simplifies the complete problem. We achieve either exact or approximated solutions by solving these algebraic equations with the proposed method. To indicate the efficiency of the proposed method, various illustrative examples are solved.