Operational calculus for bessel’s fractional equation

Abstract

This paper is intended to investigate a fractional differential Bessel’s equation of order 2α with α ∈]0, 1] involving the Riemann-Liouville derivative. We seek a possible solution in terms of power series by using operational approach for the Laplace and Mellin transform. A recurrence relation for coefficients is obtained. The existence and uniqueness of solutions is discussed via Banach fixed point theorem.