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Two Linearized Schemes for One-Dimensional Time and Space Fractional Differential Equations

Author

Listed:
  • Victor N. Orlov

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

  • Asmaa M. Elsayed

    (Department of Applied Mathematics, Moscow State University of Civil Engineering, Yaroslavskoe Shosse 26, 129337 Moscow, Russia
    Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt)

  • Elsayed I. Mahmoud

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

Abstract

This paper investigates the solution to one-dimensional fractional differential equations with two types of fractional derivative operators of orders in the range of ( 1 , 2 ) . Two linearized schemes of the numerical method are constructed. The considered FDEs are equivalently transformed by the Riemann–Liouville integral into their integro-partial differential problems to reduce the requirement for smoothness in time. The analysis of stability and convergence is rigorously discussed. Finally, numerical experiments are described, which confirm the obtained theoretical analysis.

Suggested Citation

  • Victor N. Orlov & Asmaa M. Elsayed & Elsayed I. Mahmoud, 2022. "Two Linearized Schemes for One-Dimensional Time and Space Fractional Differential Equations," Mathematics, MDPI, vol. 10(19), pages 1-16, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3651-:d:934282
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    References listed on IDEAS

    as
    1. 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.
    2. Elsayed I. Mahmoud & Viktor N. Orlov, 2021. "Numerical Solution of Two Dimensional Time-Space Fractional Fokker Planck Equation With Variable Coefficients," Mathematics, MDPI, vol. 9(11), pages 1-12, May.
    3. Asmaa M. Elsayed & Viktor N. Orlov, 2020. "Numerical Scheme for Solving Time–Space Vibration String Equation of Fractional Derivative," Mathematics, MDPI, vol. 8(7), pages 1-10, July.
    4. Ludmila Kirianova, 2020. "Modeling of Strength Characteristics of Polymer Concrete Via the Wave Equation with a Fractional Derivative," Mathematics, MDPI, vol. 8(10), pages 1-10, October.
    Full references (including those not matched with items on IDEAS)

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