Solving Fractional Oscillators Using Laplace Homotopy Analysis Method

Abstract

In this paper, we present an algorithm of the Laplace homotopy analysis method (LHAM) to obtain approximate solutions for linear and nonlinear oscillator fractional differential equations. The proposed algorithm presents a procedure of constructing the set of base functions and gives the high-order deformation equation in a simple form. The method provides the solution in the form of a rapidly convergent series. Numerical examples are used to illustrate the preciseness and effectiveness of the proposed method.