Fractional Calculus and certain integrals of Generalized multiindex Bessel function

K. S. Nisar, S. D. Purohit, R K. Parmar

Published 2017-06-25Version 1

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.