On the Conformable Triple Laplace–Sumudu Transform and Two-Dimensional Fractional Partial Differential Equations

In this work, we introduce the conformabletriple Laplace–Sumudu transform (CTLST), a novel integral transform designed to solve both linear and nonlinear conformable FPDEs. This new approach builds on the recent development of the triple Laplace–Sumudu transform and incorporates the conformable derivative to extend its applicability to fractional models. We first present the foundational definitions and key properties of the CTLST, followed by its application to a variety of two- and three-dimensional conformable FPDEs. The effectiveness of the proposed method is demonstrated through several examples, where exact and approximate solutions are derived, illustrative 3D plots are presented, and symmetry analysis is employed to verify the obtained results. The CTLST provides a promising analytical tool for tackling complex conformable FPDEs in mathematical physics and engineering.