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Axioms, Vol. 6, Pages 18: Fractional Integration and Differentiation of the Generalized Mathieu Series

Research paper by Ram Saxena, Rakesh Parmar

Indexed on: 17 Dec '17Published on: 27 Jun '17Published in: Axioms



Abstract

We aim to present some formulas for the Saigo hypergeometric fractional integral and differential operators involving the generalized Mathieu series S μ ( r ) , which are expressed in terms of the Hadamard product of the generalized Mathieu series S μ ( r ) and the Fox–Wright function p Ψ q ( z ) . Corresponding assertions for the classical Riemann–Liouville and Erdélyi–Kober fractional integral and differential operators are deduced. Further, it is emphasized that the results presented here, which are for a seemingly complicated series, can reveal their involved properties via the series of the two known functions.