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

Abstract

This paper presents a numerical technique for solving fractional di¤erential

equations by employing the multi-step Laplace Adomian decomposition method (MLADM).

The proposed scheme is only a simple modi.cation of the Adomian decomposition method,

in which it is treated as an algorithm in a sequence of small intervals (i.e. time step) for

.nding accurate approximate solutions to the corresponding problems. The MLADM is

applied for four problems to solve non-linear fractional di¤erential 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) revealed that MLADM is more e¤ective and

convenient.