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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Nisar, K.S., Purohit, S.D., Suthar, D.L., Singh, J. (2019). Fractional Order Integration and Certain Integrals of Generalized Multiindex Bessel Function. In: Singh, J., Kumar, D., Dutta, H., Baleanu, D., Purohit, S. (eds) Mathematical Modelling, Applied Analysis and Computation. ICMMAAC 2018. Springer Proceedings in Mathematics & Statistics, vol 272. Springer, Singapore. https://doi.org/10.1007/978-981-13-9608-3_10
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