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.
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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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