Comparative analysis of CFKHDM and CFTSM for the solutions of time-fractional Newell-Whitehead-Segel equations

Ali Khalouta

Abstract


Recently, the author presented an efficient technique to obtain a solution to the Newell-Whitehead-Segel equation of fractional order where the fractional derivative is in the sense ofCaputo-Fabrizio [13]. The objective of this paper is to explore a novel analytical methods for solving the same equation but involving a conformable fractional derivative operator. The methods are denoted as the conformable fractional Khalouta decomposition method (CFKHDM) and the conformable fractional Taylor series method (CFTSM). Additionally, a comparison between CFKHDM and CFTSM is performed. The accuracy and efficiency of the proposed methods are demonstrated by solving three numerical tests of the conformable time-fractional Newell-Whitehead-Segel equation. All numerical calculations were performed using the MATLAB 6 software package. These tests show that CFKHDM and CFTSM are simple, efficient and very powerful methods for finding an analytical solution to such equations. Accordingly, we believe that in the future, the current methods can be applied to compute approximate analytical solutions for a large class of conformable fractional
partial differential equations.

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DOI: https://doi.org/10.52846/ami.v53i1.2129