Investigation of Solutions for m-Dimensional Singular Fractional Pseudo-Hyperbolic Equations

In this work, we investigate the solutions of fractional singular m-dimensional pseudo-hyperbolic equations. To address these equations effectively, we generalise the Natural transform to the multi-dimensional case and examine several of its essential properties. By integrating this transform with the Adomian Decomposition Method, we formulate the Multi-Dimensional Natural Adomian (MNA) Method, which provides a systematic framework for solving the considered equations under given initial conditions. The resulting solutions are expressed as rapidly convergent series that approach either exact or highly accurate approximations. To illustrate the practicality and robustness of the proposed method, two representative examples are included, demonstrating the construction of the solution series and the derivation of approximate or exact solutions.