Description

This paper used the flexible and efficient least squares residual power series method (LSRPSM) to solve the timefractional derivative Cahn-Hilliard and Gardener equations. The LSRPSM combines the residual power series method (RPSM) and the least squares method. These calculations were found based on Caputo’s sense and the fractional Wronskian concept. Approximate solutions are found more accurately, faster, and with fewer expansion terms than the classical (RPS) method.

URL

DOI

DOI:10.1016/j.aej.2023.12.056

Brief

To sum up, our paper examines the approximated solutions of the fractional Cahn equation and Gardner equation by using LSRPS approach, which is combined with the RPSM and the least-squares approach. Approximate solutions with high accuracy with lower expansion terms have been given. Thus, we used data and figures to depict the approximate solutions. From the results obtained, we find that the present method provides convergent solutions with less processing and time than traditional RPSM and LRPSM in a simple way. Therefore, we support researchers using the LSRPS approach to obtain approximate solutions of other fractional differential equations. In the near future, we look forward to adding another method to RPSM to achieve a highaccuracy solution with lower expansion terms.

KeyWords

Fractional derivatives Least squares approximations Fractional Wronskian Residual power series method Cahn-Hilliard equation Gardner equation