CERTAIN GENERALIZED FRACTIONAL CALCULUS FORMULAS AND INTEGRAL TRANSFORMS OF $(p, q)$-EXTENDED $\tau$-HYPERGEOMETRIC FUNCTION

Print ISSN: 0972-7752 | Online ISSN: 2582-0850 | Total Downloads : 183

Abstract

In this paper, we established certain image formulas of the $(p, q)$--extended $\tau$ hypergeometric function $R^{\tau}_{\,p,q}(a,b;c;z)$ by employing Marichev-Sigo-Maeda(M-S-M) fractional integration and differentiation formulas. Corresponding special cases for the Saigo's, Riemann-Liouville and Erdelyi-Kober fractional integral and differential operators are also deduced which are earlier obtained by Solanki et al. [23]. Further certain integral transforms of the $(p, q)$--extended $\tau$ hypergeometric function $R^{\tau}_{\,p,q}(a,b;c;z)$ are established. All the results are represented in terms of the Hadamard product of the $(p, q)$--extended $\tau$ hypergeometric function $R^{\tau}_{\,p,q}(a,b;c;z)$ and the Fox-Wright function.

Keywords and Phrases

$(p, q)$-extended $\tau$--hypergeometric function; $(p,q)$ - extended hypergeometric function; Fractional calculus operators.

A.M.S. subject classification

Primary 44A20, 33B20, 33C20; Secondary 33B15; 33C05.

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