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.
Mathematics Subject Classification (2010). Primary 35R11; Secondary 34B30, 42A38, 47H10.
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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. https://doi.org/10.1007/978-3-0348-0516-2_20
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DOI: https://doi.org/10.1007/978-3-0348-0516-2_20
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