TY - JOUR AU - Al-Omari, Shrideh Khalaf PY - 2021 DA - 2021/01/07 TI - The q-Sumudu transform and its certain properties in a generalized q-calculus theory JO - Advances in Difference Equations SP - 10 VL - 2021 IS - 1 AB - 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. SN - 1687-1847 UR - https://doi.org/10.1186/s13662-020-03147-1 DO - 10.1186/s13662-020-03147-1 ID - Al-Omari2021 ER -