Theory and Applications of the Triple Laplace Transform for Local Derivative with the Mittag Leffler Kernel

Abstract

This article aims to provide a practical and reliable approach to solving fractional M-derivative partial differential equations with nine parameters that involve the Mittag-Leffler function. Several theorems have been developed to describe and express the M-derivative triple Laplace transform. Furthermore, these defined concepts and theorems are demonstrated by applying them to fractional partial differential equations. This proposed transformation appears to efficiently enable finding solutions to partial differential equations with M-derivatives that match mathematical, engineering, and physical models.