An operational method to solve fractional differential equations - Rodrigues, M. M. (2017)
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.