English

Fractional Calculus and certain integrals of Generalized multiindex Bessel function

Classical Analysis and ODEs 2019-12-17 v2

Abstract

We aim to introduce the generalized multiindex Bessel function J(βj)m,κ,b(αj)m,γ,c[z]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(βj)m,κ,b(αj)m,γ,c[z]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 pΨq(z)_{p}\Psi_{q}(z). The results presented here are of general in nature and easily reducible to new and known results.

Keywords

Cite

@article{arxiv.1706.08039,
  title  = {Fractional Calculus and certain integrals of Generalized multiindex Bessel function},
  author = {K. S. Nisar and S. D. Purohit and D. L. Suthar and J. Singh},
  journal= {arXiv preprint arXiv:1706.08039},
  year   = {2019}
}
R2 v1 2026-06-22T20:28:44.657Z