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Open AccessArticle

Fractional Integration and Differentiation of the Generalized Mathieu Series

1
Department of Mathematics and Statistics, Jai Narain Vyas University, Jodhpur-342004, Rajasthan, India
2
Department of Mathematics, Government College of Engineering and Technology, Bikaner-334004, Rajasthan, India
*
Author to whom correspondence should be addressed.
Academic Editor: Hans J. Haubold
Axioms 2017, 6(3), 18; https://doi.org/10.3390/axioms6030018
Received: 27 April 2017 / Revised: 15 June 2017 / Accepted: 22 June 2017 / Published: 27 June 2017
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PDF [243 KB, uploaded 27 June 2017]

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. View Full-Text
Keywords: Mathieu series; generalized Mathieuseries; fractional calculus operators Mathieu series; generalized Mathieuseries; fractional calculus operators
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Saxena, R.K.; Parmar, R.K. Fractional Integration and Differentiation of the Generalized Mathieu Series. Axioms 2017, 6, 18.

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