THE FRACTIONAL ANALYSIS OF (2 + 1)-DIMENSIONAL NONLINEAR TIME-FRACTIONAL ROSENAU–HYMAN MODEL USING NATURAL HOMOTOPY TRANSFORM METHOD.

This study investigates the approximate solution of the (2 + 1)-dimensional time-fractional Rosenau–Hyman model utilizing the natural homotopy transform method (NHTM). This proposed scheme is developed by coupling the natural transform (NT) and the homotopy perturbation method (HPM). We explain the fractional derivatives of the functions using the Caputo concept. We illustrate two numerical applications and compare the obtained results with the precise results of the proposed model. We present the behaviors of the obtained results for multiple orders of derivatives in two-dimensional and three-dimensional graphical representations. The convergence of the obtained solution is validated by reducing the errors over the consecutive series for the NHTM results. Consequently, the NHTM is considered the most advanced computational scheme for the approximate results of nonlinear fractional problems. [ABSTRACT FROM AUTHOR]