Solving Partial Differential Equations via the Conformable Double ARA-Sawi Transform

Abstract

This paper presents a new method the conformable double ARA-Sawi transform to solve fractional partial differential equations that arise in physics and engineering. These equations often involve derivatives based on conformable calculus, which generalizes classical derivatives to fractional orders. We explore the core properties of the transform, such as its linearity and interaction with fractional derivatives, and establish conditions for its applicability. To demonstrate its practical use, we apply the method to solve two key equations: the conformable Klein-Gordon equation, which models wave propagation in quantum fields, and the conformable telegraph equation, governing signal transmission in dissipative systems. The results highlight the transform’s ability to simplify complex fractional equations into manageable algebraic forms, offering a systematic tool for researchers. This work bridges theoretical advancements with real-world applications, paving the way for future studies in areas like nonlinear dynamics and material science.