Fractional Calculus and certain integrals of Generalized multiindex Bessel function

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.

References in corpus (1)

• Some Unified Integrals Associated with Generalized Bessel-Maitland Function