THEORY AND APPLICATIONS OF THE DOUBLE LAPLACE TRANSFORM FOR LOCAL DERİVATİVES WİTH THE MITTAG LEFFLER KERNEL

This article aims to define the 𝑀-derivative double Laplace transform, which is the general form of the six-parameter conformable derivative involving the Mittag-Leffler function. It is expressed with several theorems and will give us a useful and dependable method for solving fractional 𝑀-derivative partial differenial equations. Furthermore, the application of these given definitions and theorems to fractional partial differential equations is shown. Finding solutions to partial differential equations containing 𝑀-derivatives that can match mathematical, engineering, and physical mode ls may be accomplished with the use of this transformation.