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

Authors : Enes ATA

Pages : 512-529

Doi:10.31801/cfsuasmas.1144644

View : 26 | Download : 48

Publication Date : 2023-06-23

Article Type : Research Paper

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 $F_{A}^{insert ignore into journalissuearticles values(r);}$, $F_{B}^{insert ignore into journalissuearticles values(r);}$, $F_{C}^{insert ignore into journalissuearticles values(r);}$ and $F_{D}^{insert ignore into journalissuearticles values(r);}$. 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