Operational Calculus for Bessel’s Fractional Equation

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Abstract

This paper is intended to investigate a fractional differential Bessel’s equation of order 2α with $ \alpha \in]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.