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

Abstract

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