Operational Calculus for Bessel’s Fractional Equation
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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
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.
KeywordsFractional differential equations Riemann Liouville derivative Mellin transform Laplace transform Bessel equation.
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