The q -Sumudu transform and its certain properties in a generalized q -calculus theory

Advances in Difference Equations

article

Al-Omari, Shrideh Khalaf¹ 

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

关键词: q -delta sequences;    q -Sumudu transform;    q -convolution;    q -Boehmian;    q -calculus;   

DOI  :  10.1186/s13662-020-03147-1

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this paper we consider a generalization to the q-calculus theory in the space of q-integrable functions. We introduce q-delta sequences and develop q-convolution products to derive certain q-convolution theorem. By using the concept of q-delta sequences, we establish various axioms and set up q-spaces of generalized functions named q-Boehmian spaces. The new assigned spaces of q-generalized functions are acceptable and compatible with the classical spaces of the ordinary functions. Consequently, we extend the generalized q-Sumudu transform to the sets of q-Boehmian spaces. On top of that, we nominate the canonical q-embeddings between the q-integrable sets of functions and the q-integrable sets of q-Boehmians. Furthermore, we address the general properties of the generalized q-Sumudu transform and its inversion formula in some detail.

【 授权许可】

CC BY