Extension of generalized Fox’s H -function operator to certain set of generalized integrable functions

Advances in Difference Equations

article

Al-Omari, Shrideh Khalaf¹ 

[1] Department of Physics and Applied Sciences, Faculty of Engineering Technology, Al-Balqa Applied University

关键词: H̄ -function;    H -function;    Hypergeomatric functions;    Mittag-Leffler functions;    Boehmians;   

DOI  :  10.1186/s13662-020-02910-8

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this article, we investigate the so-called Inayat integral operator$T_{p,q}^{m,n}$ ,$p,q,m,n\in \mathbb{Z}$ ,$1\leq m\leq q$ ,$0\leq n\leq p $ , on classes of generalized integrable functions. We make use of the Mellin-type convolution product and produce a concurrent convolution product, which, taken together, establishes the Inayat integral convolution theorem. The Inayat convolution theorem and a class of delta sequences were derived and employed for constructing sequence spaces of Boehmians. Moreover, by the aid of the concept of quotients of sequences, we present a generalization of the Inayat integral operator in the context of Boehmians. Various results related to the generalized integral operator and its inversion formula are also derived.

【 授权许可】

CC BY