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Numerical Solution of Space-Time-Fractional Reaction-Diffusion Equations via the Caputo and Riesz Derivatives

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Mathematics Applied to Engineering, Modelling, and Social Issues

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 200))

Abstract

The present chapter considers the numerical solution of space-time-fractional reaction-diffusion problems used to model complex phenomena that are governed by dynamic of anomalous diffusion. The time- and space-fractional reaction-diffusion equation is modelled by replacing the first order derivative in time and the second-order derivative in space respectively with the Caputo and Riesz operators. We propose some numerical approximation schemes such as the matrix method, average central difference operator and L2 method. To give a general two-dimensional representation of the analytical solution in terms of the Mittag-Leffler function, we apply the Laplace transform technique in time and the Fourier transform method in space. The effectiveness and applicability of the proposed methods are tested on a range of practical problems that are current and recurring interests in one, two and three dimensions are chosen to cover pitfalls that may arise.

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Author information

Authors and Affiliations

  1. Faculty of Natural and Agricultural Sciences, Institute for Groundwater Studies, University of the Free State, Bloemfontein, 9300, South Africa

    Kolade M. Owolabi

  2. Department of Mathematical Sciences, Federal University of Technology, PMB 704, Akure, Ondo State, Nigeria

    Kolade M. Owolabi

  3. Department of Mathematics, Gauhati University, Guwahati, 781014, India

    Hemen Dutta

Authors
  1. Kolade M. Owolabi
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  2. Hemen Dutta
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Correspondence to Kolade M. Owolabi .

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Editors and Affiliations

  1. Department of Mathematics, University College London, London, UK

    Frank T. Smith

  2. Department of Mathematics, Gauhati University, Guwahati, Assam, India

    Hemen Dutta

  3. Department of Mathematics, Center for Mathematics of Uncertainty, Creighton University, Omaha, NE, USA

    John N. Mordeson

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Owolabi, K.M., Dutta, H. (2019). Numerical Solution of Space-Time-Fractional Reaction-Diffusion Equations via the Caputo and Riesz Derivatives. In: Smith, F.T., Dutta, H., Mordeson, J.N. (eds) Mathematics Applied to Engineering, Modelling, and Social Issues. Studies in Systems, Decision and Control, vol 200. Springer, Cham. https://doi.org/10.1007/978-3-030-12232-4_5

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  • DOI: https://doi.org/10.1007/978-3-030-12232-4_5

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