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Boundary Value Problem of Space-Time Fractional Advection Diffusion Equation

Author

Listed:
  • Elsayed I. Mahmoud

    (Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt
    Nikolskii Mathematical Institute, Peoples Friendship University of Russia, Moscow 117198, Russia)

  • Temirkhan S. Aleroev

    (Department of Applied Mathematics, Moscow State University of Civil Engineering, Yaroslavskoe Shosse, 26, Moscow 129337, Russia)

Abstract

In this article, the analytical and numerical solution of a one-dimensional space-time fractional advection diffusion equation is presented. The separation of variables method is used to carry out the analytical solution, the basis of the system eigenfunction and their corresponding eigenvalue for basic equation is determined, and the numerical solution is based on constructing the Crank-Nicolson finite difference scheme of the equivalent partial integro-differential equations. The convergence and unconditional stability of the solution are investigated. Finally, the numerical and analytical experiments are given to verify the theoretical analysis.

Suggested Citation

  • Elsayed I. Mahmoud & Temirkhan S. Aleroev, 2022. "Boundary Value Problem of Space-Time Fractional Advection Diffusion Equation," Mathematics, MDPI, vol. 10(17), pages 1-12, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3160-:d:905194
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    References listed on IDEAS

    as
    1. Rihan, F.A. & Rajivganthi, C, 2020. "Dynamics of fractional-order delay differential model of prey-predator system with Holling-type III and infection among predators," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    2. Temirkhan Aleroev, 2020. "Solving the Boundary Value Problems for Differential Equations with Fractional Derivatives by the Method of Separation of Variables," Mathematics, MDPI, vol. 8(11), pages 1-27, October.
    3. Temirkhan S. Aleroev & Asmaa M. Elsayed, 2020. "Analytical and Approximate Solution for Solving the Vibration String Equation with a Fractional Derivative," Mathematics, MDPI, vol. 8(7), pages 1-9, July.
    4. Al-Refai, Mohammed & Luchko, Yuri, 2015. "Maximum principle for the multi-term time-fractional diffusion equations with the Riemann–Liouville fractional derivatives," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 40-51.
    5. Alidousti, Javad & Ghafari, Elham, 2020. "Dynamic behavior of a fractional order prey-predator model with group defense," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
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