M-Lauricella hypergeometric functions: integral representations and solutions of fractional differential equations

Year 2023, Volume: 72 Issue: 2, 512 - 529, 23.06.2023

Enes Ata

https://doi.org/10.31801/cfsuasmas.1144644

Cited By: 3

Abstract

In this paper, using the modified beta function involving the generalized M-series in its kernel, we described new extensions for the Lauricella hypergeometric functions $F_{A}^{(r)}$, $F_{B}^{(r)}$, $F_{C}^{(r)}$ and $F_{D}^{(r)}$. Furthermore, we obtained various integral representations for the newly defined extended Lauricella hypergeometric functions. Then, we obtained solution of fractional differential equations involving new extensions of Lauricella hypergeometric functions, as examples.

Keywords

Fractional derivatives and integrals, beta function, confluent hypergeometric function, Lauricelle functions, fractional differential equations, Laplace transform

Thanks

This work was partly presented in the 4th International Conference on Pure and Applied Mathematics (ICPAM-2022) which organized by Van Yüzüncü Yıl University on June 22-23, 2022 in Van-Turkey.

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