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Mathematics 2019, 7(2), 206; https://doi.org/10.3390/math7020206

Generalized Fractional Integral Operators Pertaining to the Product of Srivastava’s Polynomials and Generalized Mathieu Series

1
Department of Mathematics, College of Arts & Science-Wadi Al-Dawaser, Prince Sattam Bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia
2
Department of Mathematics, Wollo University, Dessie 1145, Ethiopia
3
Department of Mathematics, Govt. Mahila Engg. College, Ajmer 305001, India
4
Department of HEAS (Mathematics), Rajasthan Technical University, Kota 324010, India
*
Author to whom correspondence should be addressed.
Received: 31 December 2018 / Revised: 16 February 2019 / Accepted: 20 February 2019 / Published: 23 February 2019
(This article belongs to the Special Issue Special Functions and Applications)
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Abstract

Fractional calculus image formulas involving various special functions are important for evaluation of generalized integrals and to obtain the solution of differential and integral equations. In this paper, the Saigo’s fractional integral operators involving hypergeometric function in the kernel are applied to the product of Srivastava’s polynomials and the generalized Mathieu series, containing the factor x λ ( x k + c k ) ρ in its argument. The results are expressed in terms of the generalized hypergeometric function and Hadamard product of the generalized Mathieu series. Corresponding special cases related to the Riemann–Liouville and Erdélyi–Kober fractional integral operators are also considered. View Full-Text
Keywords: generalized fractional integral operators; generalized Mathieu series; Srivastava’s polynomial; generalized hypergeometric series generalized fractional integral operators; generalized Mathieu series; Srivastava’s polynomial; generalized hypergeometric series
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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Nisar, K.; Suthar, D.; Bohra, M.; Purohit, S. Generalized Fractional Integral Operators Pertaining to the Product of Srivastava’s Polynomials and Generalized Mathieu Series. Mathematics 2019, 7, 206.

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