Multilevel M-laplace transforms applications

In our thesis, double and triple Laplace transform with M-derivative are defined. In the first part of our thesis consisting of eight chapters, it is given about the historical development of the subject. The general concepts and theorems that we will utilize in our research are discussed in the second section. Non-local fractional derivative and integral variations are defined in the third section. The concept, theorems, and single-layer Laplace transformations relating to local fractional derivative varieties, as well as local M-derivative varieties, are explained in depth and supported by examples and graphs in the fourth chapter. The definition, theorems, and examples of the corresponding values for the double and triple Laplace transforms under the M-derivative were expressed and proved in the fifth and sixth sections, which are the core of our thesis. The solutions to these examples were supported by graphs. The resulting graphs were interpreted in the seventh chapter, and a comparison between the M-derivative and the compatible derivative—a local derivative—and the classical derivative was done using the graphs as a basis. A scientific assessment was made in the eighth part taking these remarks into consideration.