Download PDF
ABSTRACT
This study applies the Natural Transform Iterative Method (NTIM) and Homotopy Perturbation Method (HPM) to approximate solutions for fractional order two-dimensional partial differential equations, focusing on the Zakharov–Kuznetsov equation. It uses Caputo fractional derivatives and Mathematica for efficient computation, producing rapidly convergent series solutions. Rigorous comparisons with existing methods affirm the method’s robustness and efficiency in solving higher-dimensional fractional order equations, demonstrating its computational efficacy and practical utility in addressing complex mathematical challenges posed by fractional order systems.
Keywords: Homotopy Perturbation Method: Caputo Derivative; Natural Transform Iterative Method; Natural Transform; Analytical Techniques