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Inverse source problem for two-term time-fractional diffusion equation with nonlocal boundary conditions

Author

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  • Derbissaly, Bauyrzhan
  • Kirane, Mokhtar
  • Sadybekov, Makhmud

Abstract

This paper explores an inverse source problem related to the heat equation, incorporating nonlocal boundary conditions and featuring two-term time-fractional derivatives. The task is to identify a source term that is independent of the spatial variable, as well as to define the temperature distribution based on energy measurements. Since the stated problem cannot be solved by direct use of the generalized Fourier method, we divide the problem into two sub-problems. The well-posedness of each problem is established through the application of the generalized Fourier method.

Suggested Citation

  • Derbissaly, Bauyrzhan & Kirane, Mokhtar & Sadybekov, Makhmud, 2024. "Inverse source problem for two-term time-fractional diffusion equation with nonlocal boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:chsofr:v:183:y:2024:i:c:s0960077924004491
    DOI: 10.1016/j.chaos.2024.114897
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    References listed on IDEAS

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    1. Li, Zhiyuan & Liu, Yikan & Yamamoto, Masahiro, 2015. "Initial-boundary value problems for multi-term time-fractional diffusion equations with positive constant coefficients," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 381-397.
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