Double ARA–Generalized Laplace Method for Solving (2 +1)–Dimensional Nonlinear Singular Pseudoparabolic Equations

This study presents a novel triple integral transformation, called the double ARA–generalized Laplace transform (DAGLT), and applies it to solve (2+1)–dimensional singular pseudoparabolic equations in both linear and nonlinear forms. The work begins by outlining the fundamental definitions, theorems, and characteristics of the single ARA and generalized Laplace transforms, then proceeds to unify them into a single framework (DAGLT). Detailed derivations of the core properties linearity, shifting, and partial derivative transforms demonstrate the theoretical soundness and broad applicability of DAGLT. Utilizing the Adomian decomposition method merged with this new transform, the paper presents an efficient procedure for obtaining closed-form or series-based solutions to challenging singular pseudoparabolic partial differential equations. Several illustrative examples showcase the effectiveness of the proposed technique, confirming that its solutions align with known results in the literature. The main advantages of the method are that it can handle singularities, and it improves the convergence. This study is promising for dealing with different models of multidimensional partial differential equations that arise in physical science and models.