Solution of Riccati Type Nonlinear Fractional Differential Equation by Homotopy Analysis Method

Abstract

The present paper deals with the application of Homotopy Analysis Method (HAM) to solve Riccati type nonlinear fractional differential equation. After the applications of various analytical methods in different forms to solve many linear and nonlinear problems (see Ref.: Liao and Shijun, Homotopy Analysis Method in Nonlinear Differential Equations. Springer-Verlag Berlin, 2012), a new method known as HAM which has a convergence control parameter  introduced in the deformation equation to reach the corresponding series solution in a much easier way. The present analysis is accompanied by numerical examples to justify its validity and efficiency. The solution obtained by this method has been compared with those obtained by Power Series Method (PSM) and Adomian Decomposition Method (ADM). The algorithm described in this paper is expected to be further employed to solve similar nonlinear problems in fractional calculus. The graphical representations of the solutions obtained by different methods are also presented for comparison of the solutions.