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

By Abdon Atangana, Adem Kılıçman. 2013

47 citations recorded by the source corpus.

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.

Subfields: Environmental Engineering, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/3adfa2a494cf433b0a997b7eae659ff973f700c5

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In Environmental Engineering

1. Udoh Akpan
2. Lanre Akinyemi
3. Olaniyi Samuel Iyiola

In Modeling and Simulation

1. Udoh Akpan
2. Lanre Akinyemi
3. Olaniyi Samuel Iyiola

In Numerical Analysis

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2. Lanre Akinyemi
3. Olaniyi Samuel Iyiola

Citations in the corpus

• Iterative methods for solving fourth‐ and sixth‐order time‐fractional Cahn‐Hillard equation (2019, methodology): “In the recent year, researchers have develop some approximate methods in solving both linear and nonlinear PDEs with fractional derivatives, such as adomian decomposition method, (ADM) [21, 25, 26], variational iteration method, (VIM) [27, 28], generalized differential transform method, (GDTM) [29, ”