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Inverse Problem for a Time Fractional Parabolic Equation with Nonlocal Boundary Conditions

Author

Listed:
  • Ebru Ozbilge

    (Department of Mathematics & Statistics, American University of the Middle East, Egaila 54200, Kuwait)

  • Fatma Kanca

    (Faculty of Engineering and Architecture, Fenerbahçe University, Istanbul 34758, Turkey)

  • Emre Özbilge

    (Department of Computer Engineering, Faculty of Engineering, Cyprus International University, North Cyprus, Mersin 10, Nicosia 99258, Turkey)

Abstract

This article considers an inverse problem of time fractional parabolic partial differential equations with the nonlocal boundary condition. Dirichlet-measured output data are used to distinguish the unknown coefficient. A finite difference scheme is constructed and a numerical approximation is made. Examples and numerical experiments, such as man-made noise, are provided to show the stability and efficiency of this numerical method.

Suggested Citation

  • Ebru Ozbilge & Fatma Kanca & Emre Özbilge, 2022. "Inverse Problem for a Time Fractional Parabolic Equation with Nonlocal Boundary Conditions," Mathematics, MDPI, vol. 10(9), pages 1-8, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1479-:d:804698
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    References listed on IDEAS

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    1. Ali Demir & Mine Aylin Bayrak & Ebru Ozbilge, 2019. "A New Approach for the Approximate Analytical Solution of Space-Time Fractional Differential Equations by the Homotopy Analysis Method," Advances in Mathematical Physics, Hindawi, vol. 2019, pages 1-12, May.
    2. Mine Aylin Bayrak & Ali Demir & Ebru Ozbilge & Soheil Salahshour, 2022. "An Improved Version of Residual Power Series Method for Space-Time Fractional Problems," Advances in Mathematical Physics, Hindawi, vol. 2022, pages 1-9, January.
    3. Gülcan Özkum & Ali Demir & Sertaç Erman & Esra Korkmaz & Berrak Özgür, 2013. "On the Inverse Problem of the Fractional Heat-Like Partial Differential Equations: Determination of the Source Function," Advances in Mathematical Physics, Hindawi, vol. 2013, pages 1-8, November.
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    Cited by:

    1. Miglena N. Koleva & Lubin G. Vulkov, 2023. "Numerical Solution of Fractional Models of Dispersion Contaminants in the Planetary Boundary Layer," Mathematics, MDPI, vol. 11(9), pages 1-21, April.
    2. Taohua Liu & Xiucao Yin & Yinghao Chen & Muzhou Hou, 2023. "A Second-Order Accurate Numerical Approximation for a Two-Sided Space-Fractional Diffusion Equation," Mathematics, MDPI, vol. 11(8), pages 1-15, April.

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