Homotopy analysis method for space‐time fractional differential equations

Abstract

PurposeIn this article, the authors aim to present the homotopy analysis method (HAM) for obtaining the approximate solutions of space‐time fractional differential equations with initial conditions.Design/methodology/approachThe series solution is developed and the recurrence relations are given explicitly. The initial approximation can be determined by imposing the initial conditions.FindingsThe comparison of the HAM results with the exact solutions is made; the results reveal that the HAM is very effective and simple. The HAM contains the auxiliary parameter h, which provides a simple way to adjust and control the convergence region of series solution. Numerical examples demonstrate the effect of changing homotopy auxiliary parameter h on the convergence of the approximate solution. Also, they illustrate the effect of the fractional derivative orders a and b on the solution behavior.Originality/valueThe idea can be used to find the numerical solutions of other fractional differential equations.