Approximate solution of the fractional differential equation via the natural decomposition method

Abstract

In today’s world, analyzing nonlinear occurrences related to physical phenomena is a hot topic. The main goal of this research is to use the natural decomposition method (NDM) of fractional order to find an approximate solution to the fractional clannish random walker’s parabolic (CRWP) equation. The proposed method gives approximate solutions that are exceptionally near the exact solution without the complication that numerous other techniques imply. Banach’s fixed-point theory is used to investigate the anticipated issue’s convergence analysis and uniqueness theorem. To ensure that the suggested technique is trustworthy and precise, numerical simulations were conducted. The results are shown in the graphs and tables. When comparing the proposed scheme’s solution to the actual solutions, it becomes clear that the scheme is efficient, systematic, and very precise when dealing with nonlinear complex phenomena.