More on the Unified Mittag–Leffler Function

Symmetry

Chahnyong Jung¹  Hafsa Yasmeen²  Ghulam Farid²  Kamsing Nonlaopon³ 

[1] Department of Business Administration, Gyeongsang National University, Jinju 52828, Korea;Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock 43600, Pakistan;Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand;

关键词: unified Mittag–Leffler function;    generalized hypergeometric function;    Fox’s H-function;    Wright generalized hypergeometric function;    Mellin transform;   

DOI  :  10.3390/sym14030523

来源: DOAJ

【 摘 要 】

Symmetry is a fascinating property of numerous mathematical notions. In mathematical analysis a function $f:[a,b]\to \mathbf{R}$ symmetric about $\frac{a+b}{2}$ satisfies the equation $f(a+b-x)=f\left(x\right)$. In this paper, we investigate the relationship of unified Mittag–Leffler function with some known special functions. We have obtained some integral transforms of unified Mittag–Leffler function in terms of Wright generalized function. We also established a recurrence relation along with another important result. Furthermore, we give formulas of Riemann–Liouville fractional integrals and fractional integrals containing unified Mittag–Leffler function for symmetric functions.

【 授权许可】

Unknown