Fractional Calculus and certain integrals of Generalized multiindex Bessel function (1706.08039v2)

Abstract: We aim to introduce the generalized multiindex Bessel function $J_{\left( \beta {j}\right) _{m},\kappa ,b}^{\left( \alpha _{j}\right){m},\gamma ,c}\left[ z\right] $ and to present some formulas of the Riemann-Liouville fractional integration and differentiation operators. Further, we also derive certain integral formulas involving the newly defined generalized multiindex Bessel function $J_{\left( \beta {j}\right) _{m},\kappa ,b}^{\left( \alpha _{j}\right){m},\gamma ,c}\left[ z\right] $. We prove that such integrals are expressed in terms of the Fox-Wright function ${p}\Psi{q}(z)$. The results presented here are of general in nature and easily reducible to new and known results.