The q-Sumudu transform and its certain properties in a generalized q-calculus theory
Shrideh Al‐Omari
Abstract
Abstract 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.