- Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
- Vol: 72 Issue: 2
- M-Lauricella hypergeometric functions: integral representations and solutions of fractional differen...
M-Lauricella hypergeometric functions: integral representations and solutions of fractional differential equations
Authors : Enes Ata
Pages : 512-529
Doi:10.31801/cfsuasmas.1144644
View : 17 | Download : 47
Publication Date : 2023-06-23
Article Type : Research Article
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