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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 381753, 11 pages
Research Article

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.

Linked References

  1. J. H. Black, J. A. Barber, and D. J. Noy, “Crosshole investigations: the method, theory and analysis of crosshole sinusoidal pressure tests in fissured rocks,” Stripa Projects Internal Reports 86-03, SKB, Stockholm, Sweden.
  2. J. F. Botha, I. Verwey van Voort, J. J. P. Viviers, W. P. Collinston, and J. C. Loock, “Karoo aquifers. Their geol­ogy, geometry and physical behaviour,” WRC Report 487/1/98, Water Research Commission, Pretoria, 1998.
  3. G. J. van Tonder, J. F. Botha, W.-H. Chiang, H. Kunstmann, and Y. Xu, “Estimation of the sustainable yields of boreholes in fractured rock formations,” Journal of Hydrology, vol. 241, no. 1-2, pp. 70–90, 2001. View at Publisher · View at Google Scholar · View at Scopus
  4. J. A. Barker, “A generalized radial flow model for hydraulic tests in fractured rock,” Water Resources Research, vol. 24, no. 10, pp. 1796–1804, 1988. View at Publisher · View at Google Scholar · View at Scopus
  5. J. Bear, Dynamics of Fluids in Porous Media, American Else­vier Environmental Science Series, Elsevier, New York, NY, USA, 1972.
  6. A. Cloot and J. F. Botha, “A generalised groundwater flow equation using the concept of non-integer order derivatives,” Water SA, vol. 32, no. 1, pp. 1–7, 2006. View at Scopus
  7. R. Courant and F. John, Introduction to Calculus and Analysis, vol. 2, John Wiley & Sons, New York, NY, USA, 1974.
  8. Y. Cherruault and G. Adomian, “Decomposition methods: a new proof of convergence,” Mathematical and Computer Modelling, vol. 18, no. 12, pp. 103–106, 1993. View at Publisher · View at Google Scholar · View at MathSciNet
  9. I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, Calif, USA, 1999. View at MathSciNet
  10. I. Podlubny, “Geometric and physical interpretation of fractional integration and fractional differentiation,” Fractional Calculus & Applied Analysis, vol. 5, no. 4, pp. 367–386, 2002. View at MathSciNet
  11. K. Adolfsson, “Nonlinear fractional order viscoelasticity at large strains,” Nonlinear Dynamics, vol. 38, no. 1–4, pp. 233–246, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  12. O. P. Agrawal, “Application of fractional derivatives in thermal analysis of disk brakes,” Nonlinear Dynamics, vol. 38, pp. 191–206, 2004. View at Publisher · View at Google Scholar
  13. G. Afken, Mathematical Methods for Physicists, Academic Press, London, UK, 1985.
  14. K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, New York, NY, USA, 1993. View at MathSciNet
  15. K. B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, New York, NY, USA, 1974. View at MathSciNet
  16. G. Adomian, “A review of the decomposition method in applied mathematics,” Journal of Mathematical Analysis and Applications, vol. 135, no. 2, pp. 501–544, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  17. A. Atangana, “New class of boundary value problems,” Information Science Letters, vol. 1, no. 2, pp. 67–76, 2012. View at Publisher · View at Google Scholar
  18. G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic, Dodrecht, The Netherlands, 1994. View at MathSciNet
  19. Y. Cherruault, “Convergence of Adomian's method,” Kybernetes, vol. 18, no. 2, pp. 31–38, 1989. View at Publisher · View at Google Scholar · View at MathSciNet