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Advances in Harmonic Analysis and Operator Theory
Volume 229 of the series Operator Theory: Advances and Applications pp 357370
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
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. Title
 Operational Calculus for Bessel’s Fractional Equation
 Book Title
 Advances in Harmonic Analysis and Operator Theory
 Book Subtitle
 The Stefan Samko Anniversary Volume
 Pages
 pp 357370
 Copyright
 2013
 DOI
 10.1007/9783034805162_20
 Print ISBN
 9783034805155
 Online ISBN
 9783034805162
 Series Title
 Operator Theory: Advances and Applications
 Series Volume
 229
 Publisher
 Springer Basel
 Copyright Holder
 Springer Basel
 Additional Links
 Topics
 Keywords

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

 Alexandre Almeida ^{(ID1)}
 Luís Castro ^{(ID2)}
 FrankOlme Speck ^{(ID3)}
 Editor Affiliations

 ID1. , Departamento de Matemática, Universidade de Aveiro
 ID2. , Departamento de Matemática, Universidade de Aveiro
 ID3. Instituto Superior Tecnico, Depto. Matematica, Universidade Tecnica Lisboa
 Authors

 M. M. Rodrigues ^{(1)}
 N. Vieira ^{(2)}
 S. Yakubovich ^{(3)}
 Author Affiliations

 1. Center for Research and Development in Mathematics and Applications Department of Mathematics, University of Aveiro Campus Universitário de Santiago, 3810193, Aveiro, Portugal
 2. Center of Mathematics of University of Porto Faculty of Science, University of Porto, Rua do Campo Alegre 687, 4169007, Porto, Portugal
 3. Department of Mathematics, Faculty of Science, University of Porto, Rua do Campo Alegre 687, 4169007, Porto, Portugal
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