ON Q-ANALOGUES REGARDING AL-ZUGHAIR TRANSFORM

Abstract

Solving difficult differential equations depends critically upon integral transforms such like Laplace,, and Fourier. through adding q-calculus, the newly proposed q-Al-Zughair transform increases the range regarding the Al-Zughair transform, and becomes more flexible within the favor of the solving equations within q-deformed systems, including quantum mechanics. This work applies it towards ordinary, and partial differential equations, and derives the q-Al-Zughair transform, and investigates its essential features, including linearity, and inversion. Comparative study shows how better this novel method happens towards being than conventional transforms. The results imply, that broadening the applications regarding integral transforms within many domains may benefit coming from the q-Al-Zughair transform.