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

Mridula Purohit, Sumair Mushtaq

Abstract


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.

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Published: 2020-08-03

How to Cite this Article:

Mridula Purohit, Sumair Mushtaq, Applications of Laplace-Adomian decomposition method for solving time-fractional advection dispersion equation, J. Math. Comput. Sci., 10 (2020), 1960-1968

Copyright © 2020 Mridula Purohit, Sumair Mushtaq. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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