Chapter

Advances in Harmonic Analysis and Operator Theory

Volume 229 of the series Operator Theory: Advances and Applications pp 357-370

Date:

Operational Calculus for Bessel’s Fractional Equation

  • M. M. RodriguesAffiliated withCenter for Research and Development in Mathematics and Applications Department of Mathematics, University of Aveiro Campus Universitário de Santiago Email author 
  • , N. VieiraAffiliated withCenter of Mathematics of University of Porto Faculty of Science, University of Porto
  • , S. YakubovichAffiliated withDepartment of Mathematics, Faculty of Science, University of Porto

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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.

Keywords

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