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An Operator-Based Scheme for the Numerical Integration of FDEs

Author

Listed:
  • Inga Timofejeva

    (Center for Nonlinear Systems, Kaunas University of Technology, Studentu, 50-147 Kaunas, Lithuania)

  • Zenonas Navickas

    (Center for Nonlinear Systems, Kaunas University of Technology, Studentu, 50-147 Kaunas, Lithuania)

  • Tadas Telksnys

    (Center for Nonlinear Systems, Kaunas University of Technology, Studentu, 50-147 Kaunas, Lithuania)

  • Romas Marcinkevicius

    (Department of Software Engineering, Kaunas University of Technology, Studentu, 50-415 Kaunas, Lithuania)

  • Minvydas Ragulskis

    (Center for Nonlinear Systems, Kaunas University of Technology, Studentu, 50-147 Kaunas, Lithuania)

Abstract

An operator-based scheme for the numerical integration of fractional differential equations is presented in this paper. The generalized differential operator is used to construct the analytic solution to the corresponding characteristic ordinary differential equation in the form of an infinite power series. The approximate numerical solution is constructed by truncating the power series, and by changing the point of the expansion. The developed adaptive integration step selection strategy is based on the controlled error of approximation induced by the truncation. Computational experiments are used to demonstrate the efficacy of the proposed scheme.

Suggested Citation

  • Inga Timofejeva & Zenonas Navickas & Tadas Telksnys & Romas Marcinkevicius & Minvydas Ragulskis, 2021. "An Operator-Based Scheme for the Numerical Integration of FDEs," Mathematics, MDPI, vol. 9(12), pages 1-17, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1372-:d:574462
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    References listed on IDEAS

    as
    1. Kheybari, Samad, 2021. "Numerical algorithm to Caputo type time–space fractional partial differential equations with variable coefficients," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 66-85.
    2. Acay, Bahar & Inc, Mustafa, 2021. "Fractional modeling of temperature dynamics of a building with singular kernels," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    3. Dubey, Ved Prakash & Dubey, Sarvesh & Kumar, Devendra & Singh, Jagdev, 2021. "A computational study of fractional model of atmospheric dynamics of carbon dioxide gas," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    4. Tarasov, Vasily E., 2020. "Fractional econophysics: Market price dynamics with memory effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    5. Navickas, Z. & Telksnys, T. & Marcinkevicius, R. & Ragulskis, M., 2017. "Operator-based approach for the construction of analytical soliton solutions to nonlinear fractional-order differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 625-634.
    6. H. Jafari & H. Tajadodi, 2010. "He's Variational Iteration Method for Solving Fractional Riccati Differential Equation," International Journal of Differential Equations, Hindawi, vol. 2010, pages 1-8, March.
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