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Research on Adomian decomposition method and its application in the fractional order differential equations

Jing-Guo Qu, Yu-Huan Cui, Guan-Chen Zhou

This paper mainly studies the basic principle of Adomian decomposition method and uses the principle to solve differential equations of fractional in order to get the approximate analytical solution in series form. The application of this method is extended to fractional order nonlinear convection diffusion equation of time. Using this method, the paper gets the solution of the equation and the solution satisfying the initial conditions. The result is the extension of the standard diffusion equation solved by former scholars. Compared with the standard methods, this numerical solution of this method can obtain approximate precision analytical solutions and the convergence is very fast. It does not require discretization and a large amount of computation.