# Operational Calculus for Bessel’s Fractional Equation

Conference paper

- First Online:

DOI: 10.1007/978-3-0348-0516-2_20

- Cite this paper as:
- Rodrigues M.M., Vieira N., Yakubovich S. (2013) Operational Calculus for Bessel’s Fractional Equation. In: Almeida A., Castro L., Speck FO. (eds) Advances in Harmonic Analysis and Operator Theory. Operator Theory: Advances and Applications, vol 229. Birkhäuser, Basel

## 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.

### Keywords

Fractional differential equations Riemann Liouville derivative Mellin transform Laplace transform Bessel equation.## Preview

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## Copyright information

© Springer Basel 2013