Solution of time-fractional Cahn–Hilliard equation with reaction term using homotopy analysis method

Abstract

In this article, the approximate analytical solution of the time-fractional Cahn–Hilliard equation with quadratic form of the source/sink term is obtained using the powerful homotopy analysis method, which permits us to select a convergence control parameter that minimizes residual errors. The concerned method is more general in theory and widely valid in practice to solve nonlinear problems even for fractional order systems as it provides a convenient way to guarantee the convergence of the approximate series. The results have been given to show the effect of the reaction term on the solution profile in both fractional and standard order cases for different particular cases. The main feature of this study is the authentication that only a few iterations are required to obtain the accurate approximate solution of the present mathematical model. This is justified through error analysis for both fractional and standard order cases. This striking feature of savings in time is exhibited through graphical presentations of the numerical values when the system passes from standard order to fractional order in the presence or absence of the reaction term.