Towards a new triple integral transform (Laplace–ARA–Sumudu) with applications

The main objective of this work is to introduce a novel generalization double transformations called the triple Laplace–ARA–Sumudu transform (TLARAST). This hybrid transformation extends concepts Laplace–Sumudu, Laplace–ARA and ARA–Sumudu transforms into transform. article provides definition TLARAST investigates its fundamental properties, including existence, inverses related theorems. Furthermore, new results concerning for partial derivatives theorem multi-convolution are introduced discussed. practicality efficacy demonstrated by applying it solve various types differential equations with significant applications in physics other scientific fields, such as heat equation, Laplace Poisson equation wave equation. solutions illustrated through figures created using Mathematica software. Overall, study underscores usefulness efficiency solving involving multiple variables.