Abstract

Motivated by a recent work on Marichev-Saigo-Maeda fractional calculus operators associated with the generalized k-Struve function(Seema Kabra et al. [19] in Applied Mathematics and Nonlinear Sciences, 5(2),593-602), this paper establishes four theorem by using Marichev -Maeda-Saigo fractional integral and derivative operators involving the product of the $(p,q)$-Extended Bessel function and Generalized k-Struve function, supported by serveral auxillary lemmas. The results are expressed in terms of the $_{r+k}F_{s+k}$ and generalized k-Wright function $ {_r\psi_s}^k$. Some new and known results are also obtained in special cases of main results.

Keywords and Phrases

MSM Fractional Calculus Operator, $(p,q)$-Extended Bessel function and Generalized k-Struve function, $(p,q)$-Extended generalized hypergeometric function and Generalized k-Wright function.

A.M.S. subject classification

Primary 26A33, Secondary 33C45, 33E12, 44A20.

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