A new recursive scheme for solving the general fractional differential equation of the nonlinear Lienard’s equation

The purpose of this paper is to solve an initial-value problem for the general fractional differential equation of the nonlinear Lienard's equation.

A new recursive scheme is presented by combining the Adomian decomposition method with a magnificent recurrence formula and via the solutions of the well-known generalized Abel equation.

It is shown that the proposed method may offer advantages in computing the components yn; n = 1; 2; … in an easily computed formula. Also, the numerical experiments show that with few iterations of the recursive method, this technique converges swiftly and accurately.

The approach is original, and a reasonably accurate solution can be achieved with only two components. Moreover, the proposed method can be applied to several nonlinear models in science and engineering.