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Efficient numerical simulation of non-integer-order space-fractional reaction-diffusion equation via the Riemann-Liouville operator

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Abstract.

In this work, we are concerned with the solution of non-integer space-fractional reaction-diffusion equations with the Riemann-Liouville space-fractional derivative in high dimensions. We approximate the Riemann-Liouville derivative with the Fourier transform method and advance the resulting system in time with any time-stepping solver. In the numerical experiments, we expect the travelling wave to arise from the given initial condition on the computational domain \((-\infty, \infty)\), which we terminate in the numerical experiments with a large but truncated value of L. It is necessary to choose L large enough to allow the waves to have enough space to distribute. Experimental results in high dimensions on the space-fractional reaction-diffusion models with applications to biological models (Fisher and Allen-Cahn equations) are considered. Simulation results reveal that fractional reaction-diffusion equations can give rise to a range of physical phenomena when compared to non-integer-order cases. As a result, most meaningful and practical situations are found to be modelled with the concept of fractional calculus.

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Authors and Affiliations

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

    Kolade M. Owolabi

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

    Kolade M. Owolabi

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Correspondence to Kolade M. Owolabi.

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Owolabi, K.M. Efficient numerical simulation of non-integer-order space-fractional reaction-diffusion equation via the Riemann-Liouville operator. Eur. Phys. J. Plus 133, 98 (2018). https://doi.org/10.1140/epjp/i2018-11951-x

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