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

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.