Towards solving linear fractional differential equations with Hermite operational matrix

This paper presents the derivation of a new operational matrix of Caputo fractional derivatives through Hermite polynomials with Tau method to solve a set of fractional differential equations (FDEs). The proposed algorithm is intended to solve linear type of FDEs with the pre-defined conditions into a matrix form for redefining the complete problem as a system of a algebraic equations.The proposed strategy is then applied to solve the simplified FDEs in linear form. To assess the performance of the proposed method, exact and approximate solutions for a number of illustrative examples are obtained which prove the effectiveness of the idea.