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arXiv · 1706.08039

Fractional Calculus and certain integrals of Generalized multiindex Bessel function

K. S. Nisar·S. D. Purohit·D. L. Suthar·J. Singh
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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.

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K. S. Nisar, S. D. Purohit, D. L. Suthar, J. Singh. 2017-06-25. Fractional Calculus and certain integrals of Generalized multiindex Bessel function. https://arxiv.org/abs/1706.08039

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