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Analytical Solutions of the Space-Time Fractional Derivative of Advection Dispersion Equation

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  • Abdon Atangana
  • Adem Kilicman

Abstract

Fractional advection-dispersion equations are used in groundwater hydrology to model the transport of passive tracers carried by fluid flow in porous medium. A space-time fractional advection-dispersion equation (FADE) is a generalization of the classical ADE in which the first-order space derivative is replaced with Caputo or Riemann-Liouville derivative of order , and the second-order space derivative is replaced with the Caputo or the Riemann-Liouville fractional derivative of order . We derive the solution of the new equation in terms of Mittag-Leffler functions using Laplace transfrom. Some examples are given. The results from comparison let no doubt that the FADE is better in prediction than ADE.

Suggested Citation

  • Abdon Atangana & Adem Kilicman, 2013. "Analytical Solutions of the Space-Time Fractional Derivative of Advection Dispersion Equation," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-9, April.
    • Handle: RePEc:hin:jnlmpe:853127
    DOI: 10.1155/2013/853127
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    Cited by:

    1. Iqbal, Muhammad S. & Seadawy, Aly R. & Baber, Muhammad Z. & Qasim, Muhammad, 2022. "Application of modified exponential rational function method to Jaulent–Miodek system leading to exact classical solutions," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Tahereh Eftekhari & Jalil Rashidinia, 2023. "An Investigation on Existence, Uniqueness, and Approximate Solutions for Two-Dimensional Nonlinear Fractional Integro-Differential Equations," Mathematics, MDPI, vol. 11(4), pages 1-29, February.

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