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Subordination Approach to Space-Time Fractional Diffusion

Author

Listed:
  • Emilia Bazhlekova

    (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev str., Bld. 8, Sofia 1113, Bulgaria)

  • Ivan Bazhlekov

    (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev str., Bld. 8, Sofia 1113, Bulgaria)

Abstract

The fundamental solution to the multi-dimensional space-time fractional diffusion equation is studied by applying the subordination principle, which provides a relation to the classical Gaussian function. Integral representations in terms of Mittag-Leffler functions are derived for the fundamental solution and the subordination kernel. The obtained integral representations are used for numerical evaluation of the fundamental solution for different values of the parameters.

Suggested Citation

  • Emilia Bazhlekova & Ivan Bazhlekov, 2019. "Subordination Approach to Space-Time Fractional Diffusion," Mathematics, MDPI, vol. 7(5), pages 1-12, May.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:415-:d:229697
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    References listed on IDEAS

    as
    1. Tomovski, Živorad & Sandev, Trifce & Metzler, Ralf & Dubbeldam, Johan, 2012. "Generalized space–time fractional diffusion equation with composite fractional time derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(8), pages 2527-2542.
    2. Boyadjiev, Lyubomir & Luchko, Yuri, 2017. "Mellin integral transform approach to analyze the multidimensional diffusion-wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 127-134.
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    Cited by:

    1. Trifce Sandev & Viktor Domazetoski & Alexander Iomin & Ljupco Kocarev, 2021. "Diffusion–Advection Equations on a Comb: Resetting and Random Search," Mathematics, MDPI, vol. 9(3), pages 1-24, January.

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