On the Double of the Laplace–Mayan Transformation and Its Properties With Applications

In this study, we have been able to extend the concept of a Mayan integral transform for a one-dimensional Mayan integral transform to a two dimensional, also called the double Laplace–Mayan integral transform. Some key concepts, definitions, and theorems for the double Laplace–Mayan transform have also been defined in this study. To verify the effectiveness, accuracy, and applicability of the newly defined Mayan integral transform, this study has also used the Mayan integral transform for solving partial differential equations (PDEs). The use of the double Laplace-integral transform in this study has been almost indispensable for many authors in solving partial differential equations, and among the most effective ways in which the double integral transform can be introduced in detail in solving partial differential equations is by proposing a solution for a PDE and reducing it to an algebraic problem, specifically solving an algebraic equation. Some of the most indispensable PDEs are the Laplace, Poisson, Wave, Heat, Telegraph, and many more. This newly introduced double Mayan integral transform involving an operator “DLM·†would then have the transform function given as follows: DLMfy,z=Ts,p,β,α=1/siβ∫0∞∫0∞fy,ze−pye−siαzdzdy.