Analytical Properties of a Novel Fractional Integral Transform with Mittag Leffler Kernel

This paper introduces a novel integral transform designed for functions in class A, offering several distinct advantages over traditional transforms like the Laplace transform. Key benefits include a flexible s-domain, pole-shifting capabilities, and a broader domain of analyticity, which enhance the transform’s versatility in addressing complex problems. Initially defined for continuous and smooth functions, the transform’s applicability is extended to a wider class of functions, including fractional-order differential equations, by modifying the kernel with the Mittag-Leffler function. The Mittag-Leffler function is particularly advantageous over other special functions due to its ability to effectively capture fractional-order dynamics, which is essential for modeling systems with memory and hereditary properties. This modification addresses the limitations of traditional methods in fractional-order systems. A detailed theoretical exploration of the new transform’s properties is conducted, and its computational efficiency is demonstrated through applications such as the fractional RL circuit problem. The results highlight the transform’s potential as a powerful tool in solving fractional-order linear differential equations (FDEs).