Abstract
Due to the memory trait of the fractional calculus, numerical or analytical solution of higher order becomes very difficult even impossible to obtain in real engineering problems. Recently, a new and convenient way was suggested to calculate the Adomian series and the higher order approximation was realized. In this paper, the Adomian decomposition method is applied to nonlinear fractional differential equation and the error analysis is given which shows the convenience.
Highlights
The fractional calculus has frequently appeared in various applied areas and has become an increasing interesting topic in the past decades [1,2,3,4,5,6,7]
The often used numerical methods are the fractional difference method [8,9,10] and the predictor corrector method [11,12,13] and others as well as the analytical methods such as the variational iteration method (VIM) [14,15,16,17] and the Adomian decomposition method (ADM) [17,18,19,20,21] and others. These methods are developed from original versions for ordinary differential equation of the integer order equation
We present our analytical schemes using the convenient Adomian series, Laplace transform, and Pade approximation
Summary
The fractional calculus has frequently appeared in various applied areas and has become an increasing interesting topic in the past decades [1,2,3,4,5,6,7]. The often used numerical methods are the fractional difference method [8,9,10] and the predictor corrector method [11,12,13] and others as well as the analytical methods such as the variational iteration method (VIM) [14,15,16,17] and the Adomian decomposition method (ADM) [17,18,19,20,21] and others These methods are developed from original versions for ordinary differential equation of the integer order equation. We define the residual function and give the error analysis and investigate the validness of the iteration formulae
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