The α - Laplace Elzaki Integral Transform on Time Scales

Abstract

This paper introduces the α-Laplace Elzaki transform, a significant generalization of the nabla version on time scales. This transform rigorously established the fundamental properties, including the existence theorem, linearity, and the convolution theorem. Additionally, we derive the key derivative characteristics that underpin its functionality. The α-Laplace Elzaki transform combines techniques for discrete, continuous, and hybrid systems and is a powerful approach for solving partial dynamic equations over time scales.