Analytical solution of the linear fractional differential equation by Adomian decomposition method☆

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Abstract

In this paper, we consider the n-term linear fractional-order differential equation with constant coefficients and obtain the solution of this kind of fractional differential equations by Adomian decomposition method. With the equivalent transmutation, we show that the solution by Adomian decomposition method is the same as the solution by the Green's function. Finally, we illustrate our result with some examples.

MSC

26A33
65L05

Keywords

Fractional derivative
Fractional integral
Adomian decomposition method
Green's function

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Project Supported by a National Key Basic Research Project of China (Grant no. 2004CB318000) and the Natural Science Foundation of China (Grant no. 10371090) and the Natural Science Foundation of Zhejiang Province (Grant no. M103043).

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