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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 381753, 11 pages
Analytical Solutions of a Space-Time Fractional Derivative of Groundwater Flow Equation
Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, P.O. Box 399, Bloemfontein, South Africa
Received 5 September 2013; Accepted 12 September 2013; Published 21 January 2014
Academic Editor: Hossein Jafari
Copyright © 2014 Abdon Atangana and P. D. Vermeulen. 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.
Citations to this Article [11 citations]
The following is the list of published articles that have cited the current article.
- Abdon Atangana, and Suares Clovis Oukouomi Noutchie, “On Multi-Laplace Transform for Solving Nonlinear Partial Differential Equations with Mixed Derivatives,” Mathematical Problems in Engineering, vol. 2014, pp. 1–9, 2014.
- Emile Franc Doungmo Goufo, Riëtte Maritz, and Stella Mugisha, “Existence Results for a Michaud Fractional, Nonlocal, and Randomly Position Structured Fragmentation Model,” Mathematical Problems in Engineering, vol. 2014, pp. 1–8, 2014.
- Emile Franc Doungmo Goufo, and Stella Mugisha, “Mathematical Solvability of a Caputo Fractional Polymer Degradation Model Using Further Generalized Functions,” Mathematical Problems in Engineering, vol. 2014, pp. 1–5, 2014.
- Abdon Atangana, Seyma Tuluce Demiray, and Hasan Bulut, “Modelling the Nonlinear Wave Motion within the Scope of the Fractional Calculus,” Abstract and Applied Analysis, vol. 2014, pp. 1–7, 2014.
- Abdon Atangana, and S. C. Oukouomi Noutchie, “A Modified Groundwater Flow Model Using the Space Time Riemann-Liouville Fractional Derivatives Approximation,” Abstract and Applied Analysis, vol. 2014, pp. 1–7, 2014.
- Emile Franc Doungmo Goufo, Suares Clovis Oukouomi Noutchie, and Stella Mugisha, “A Fractional SEIR Epidemic Model for Spatial and Temporal Spread of Measles in Metapopulations,” Abstract and Applied Analysis, vol. 2014, pp. 1–6, 2014.
- Leilei Wei, and Xindong Zhang, “A Computational Study of an Implicit Local Discontinuous Galerkin Method for Time-Fractional Diffusion Equations,” Abstract and Applied Analysis, vol. 2014, pp. 1–11, 2014.
- Ninghu Su, Paul N. Nelson, and Sarah Connor, “The distributed-order fractional diffusion-wave equation of groundwater flow: Theory and application to pumping and slug tests,” Journal of Hydrology, 2015.
- Abdon Atangana, Dumitru Baleanu, and Ahmed Alsaedi, “New properties of conformable derivative,” Open Mathematics, vol. 13, pp. 889–898, 2015.
- Abdon Atangana, “Exact solution of the time-fractional groundwater flow equation within a leaky aquifer equation,” Journal Of Vibration And Control, vol. 22, no. 7, pp. 1749–1756, 2016.
- Abdon Atangana, and Rubayyi Alqahtani, “Modelling the Spread of River Blindness Disease via the Caputo Fractional Derivative and the Beta-derivative,” Entropy, vol. 18, no. 2, pp. 40, 2016.