Fractional Integration and Differentiation of the Generalized Mathieu Series
Department of Mathematics and Statistics, Jai Narain Vyas University, Jodhpur-342004, Rajasthan, India
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
Received: 27 April 2017 / Revised: 15 June 2017 / Accepted: 22 June 2017 / Published: 27 June 2017
We aim to present some formulas for the Saigo hypergeometric fractional integral and differential operators involving the generalized Mathieu series
, which are expressed in terms of the Hadamard product of the generalized Mathieu series
and the Fox–Wright function
. 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.
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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MDPI and ACS Style
Saxena, R.K.; Parmar, R.K. Fractional Integration and Differentiation of the Generalized Mathieu Series. Axioms 2017, 6, 18.
Saxena RK, Parmar RK. Fractional Integration and Differentiation of the Generalized Mathieu Series. Axioms. 2017; 6(3):18.
Saxena, Ram K.; Parmar, Rakesh K. 2017. "Fractional Integration and Differentiation of the Generalized Mathieu Series." Axioms 6, no. 3: 18.
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