Numerical treatment of multi-term time fractional nonlinear KdV equations with weakly singular solutions

The main aim of this work is to construct an efficient recursive numerical technique for solving multi-term time fractional nonlinear KdV equation. The fractional derivatives are defined in Caputo sense. A modified Laplace decomposition method is introduced to approximate the solution. The Adomian polynomials play an important role to execute such a recursive process. In addition, the mathematical importance and some applications of KdV equation are discussed. The approximate solution obtained by the proposed method can be expressed in the form of an infinite convergent series. The experimental evidences demonstrate the effectiveness of the proposed method.