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.

在本文中，我们考虑推广到q中的空间演算理论q -integrable功能。我们引入q -delta序列，并开发q-卷积积以推导某些q-卷积定理。通过使用这个概念q -δ序列，我们建立不同的公理，并成立q -spaces的命名广义函数q -Boehmian空间。q广义函数的新分配空间是可以接受的，并且与普通函数的经典空间兼容。因此，我们扩展了广义q -Sumudu转换到套q-波希米亚空间。最重要的是，我们提名的规范q之间-embeddings q -integrable套的功能和q -integrable套q -Boehmians。此外，我们更详细地讨论了广义q -Sumudu变换的一般性质及其反演公式。