SOLVING 2D MATHEMATICAL MODELS ARISING IN APPLIED SCIENCES WITH CAPUTO DERIVATIVES VIA HYBRID HPM

This paper presents a novel approach for solving 2D mathematical models arising in applied sciences, specifically focusing on 2-dimensional time-fractional order Klein-Gordon (TFKGE) and sine-Gordon equations (TFSGE) using the Sumudu transform-homotopy perturbation method (STHPM). The amalgamation of the Sumudu transform with the homotopy perturbation method provides an effective analytical technique for tackling these time-fractional order partial differential equations. The solutions obtained illustrate the precision and efficiency of the method, offering valuable insights for modelling complex physical systems. In this study, we also solve the same numerical problems using the variational iteration method and perform a comparative analysis of the results. This study advances the application of fractional calculus methods to challenging problems in theoretical and applied physics.