An operational method to solve fractional differential equations

Abstract

In this paper, we present an operational method for solving two fractional equations, namely, the Legendre and the Laguerre equations. Based on operational approach for the Laplace and Mellin, we obtain a particular solution as a generalized power series for both equations, where the fractional derivatives are defined in the Riemann-Liouville sense. We prove the existence and uniqueness of solutions via Banach fix point theorem.