Solving nonlinear fractional differential equation using a multi-step Laplace Adomian decomposition method

This paper presents a numerical technique for solving fractional differential equations by employing the multi-step Laplace Adomian decomposition method (MLADM). The proposed scheme is only a simple modification of the Adomian decomposition method, in which it is treated as an algorithm in a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the corresponding problems. This method was applied in four examples to solve non-linear fractional differential equations which were presented as fractional initial value problems. The fractional derivatives are described in the Caputo sense. Figurative comparisons between the MLADM and the classical fourth-order Runge Kutta method (RK4) reveal that this modified method is more effective and convenient.