On the extended Wright hypergeometric matrix function and its properties

Authors : Halil GEZER, Cem KAANOGLU

Pages : 606-617

Doi:10.31801/cfsuasmas.1147745

View : 25 | Download : 45

Publication Date : 2023-09-30

Article Type : Research Paper

Abstract :Recently, Bakhet et al. [9] presented the Wright hypergeometric matrix function $_{2}R_{1}^{insert ignore into journalissuearticles values(\\tau );}insert ignore into journalissuearticles values(A,B;C;z);$ and derived several properties. Abdalla [6] has since applied fractional operators to this function. In this paper, with the help of the generalized Pochhammer matrix symbol $insert ignore into journalissuearticles values(A;B);_{n}$ and the generalized beta matrix function $\\mathcal{B}insert ignore into journalissuearticles values(P,Q;\\mathbb{X});$, we introduce and study an extended form of the Wright hypergeometric matrix function, $_{2}R_{1}^{insert ignore into journalissuearticles values(\\tau );}insert ignore into journalissuearticles values(insert ignore into journalissuearticles values(A,\\mathbb{A});,B;C;z;\\mathbb{X});.$ We establish several potentially useful results for this extended form, such as integral representations and fractional derivatives. We also derive some properties of the corresponding incomplete extended Wright hypergeometric matrix function.
Keywords : Wright hypergeometric matrix function, generalized hypergeometric functions, Riemann Liouville fractional derivative