Adapting semi-analytical treatments to the time-fractional derivative Gardner and Cahn-Hilliard equations

Abstract

This paper used the flexible and efficient least squares residual power series method (LSRPSM) to solve the time-fractional 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.

Keywords

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