Operational Calculus for Bessel’s Fractional Equation

Conference paper

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

Part of the Operator Theory: Advances and Applications book series (OT, volume 229)
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. 

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Center for Research and Development in Mathematics and Applications Department of MathematicsUniversity of Aveiro Campus Universitário de SantiagoAveiroPortugal
  2. 2.Center of Mathematics of University of Porto Faculty of ScienceUniversity of PortoPortoPortugal
  3. 3.Department of Mathematics, Faculty of ScienceUniversity of PortoPortoPortugal

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