NOVEL APPROXIMATIONS TO THE FRACTIONAL NEWELL-WHITEHEAD-SEGEL EQUATIONS WITHIN CAPUTO OPERATOR

This analytical study aims to analyze and solve some different forms for the fractional Newell-Whitehead-Segel equation (FNWSE) utilizing the Caputo operator, employing the Mohand/Laplace transform iterative method (MTIM), and the Mohand/Laplace residual power series method (MRPSM). Thus, by utilizing these advanced mathematical techniques, we can obtain precise analytical approximations for the FNWSE and examine them numerically and graphically in tabular and graphical formats. Furthermore, by graphically comparing the obtained analytical approximate solutions with the exact solutions for the integer cases, we can validate the precision of the generated approximations. Moreover, the absolute error of the obtained approximations can be estimated and numerically discussed to assess the efficacy of the proposed approaches and validate the high accuracy of the derived approximations. As such, the present study demonstrates the reliability of the proposed methods for analyzing and solving more complicated fractional differential equations. Consequently, the results gained can contribute to bridging the existing gap in the literature on fractional calculus, primarily through the application of MTIM and MRPSM in addressing nonlinear fractional equations. Furthermore, the suggested methodologies can be utilized to simulate numerous nonlinear phenomena occurring in multiplasma systems by examining various wave equations in their fractional representations that describe the propagation of nonlinear waves in these systems.