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Applications of Laplace-Adomian decomposition method for solving time-fractional advection dispersion equation

In this paper, a space-time fractional partial differential equation, obtained from the standard partial differential equation by replacing the second order space-derivative by a fractional derivative of order β > 0 and the first order time-derivative by a fractional derivative of order α > 0 has been recently treated by a number of authors. A time fractional advection-dispersion equation is obtained from the standard advection-dispersion equation by replacing the first order derivative in time by a fractional derivative in time of order α (0 < α ≤ 1). In the present paper, the solution of the analytical dispersion equation is derived using Laplace-Adomian Decomposition Method (LADM). This method has higher convergences as the solutions both of fractional order and integral are obtained in the form of series. In this method the Caputo derivatives are used to define fractional order derivatives. To confirm validity of this method illustrative examples are given.