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Inverse random source problem for the stochastic Caputo–Hadamard time-fractional diffusion equation driven by fractional Brownian motion

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  • Yang, Fan
  • Li, Si-Ying
  • Li, Xiao-Xiao

Abstract

This study focuses on the inverse random source problem for the Caputo–Hadamard time-fractional diffusion equation driven by fractional Brownian motion. First, the well-posedness of the solution to the direct problem is established under certain conditions. For the inverse problem, the ill-posedness of recovering the source term is analyzed from the perspectives of expectation and variance. To address the ill-posedness, an iterative fractional Tikhonov–Landweber method is employed, and both a priori and a posteriori error estimates are derived. Finally, numerical examples are provided to demonstrate the effectiveness of the method and the accuracy of the theoretical results.

Suggested Citation

  • Yang, Fan & Li, Si-Ying & Li, Xiao-Xiao, 2025. "Inverse random source problem for the stochastic Caputo–Hadamard time-fractional diffusion equation driven by fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 201(P2).
    • Handle: RePEc:eee:chsofr:v:201:y:2025:i:p2:s0960077925012469
    DOI: 10.1016/j.chaos.2025.117233
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    References listed on IDEAS

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    1. Zhiwei Yang & Xiangcheng Zheng & Hong Wang, 2022. "Well-Posedness And Regularity Of Caputo–Hadamard Time-Fractional Diffusion Equations," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(01), pages 1-13, February.
    2. Cao, Dingding & Li, Changpin, 2025. "Quenching phenomenon in the Caputo–Hadamard time-fractional Kawarada problem: Analysis and computation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 233(C), pages 21-38.
    3. Qiao, Li & Yang, Fan & Li, Xiaoxiao, 2024. "Simultaneous identification of the unknown source term and initial value for the time fractional diffusion equation with local and nonlocal operators," Chaos, Solitons & Fractals, Elsevier, vol. 189(P1).
    4. Bashir Ahmad & Ahmed Alsaedi & Sotiris K. Ntouyas & Jessada Tariboon, 2017. "Hadamard-Type Fractional Differential Equations, Inclusions and Inequalities," Springer Books, Springer, number 978-3-319-52141-1, October.
    5. Chenyu Zhang & Fan Yang & Xiaoxiao Li, 2024. "Two Regularization Methods for Identifying the Spatial Source Term Problem for a Space-Time Fractional Diffusion-Wave Equation," Mathematics, MDPI, vol. 12(2), pages 1-28, January.
    6. Garra, Roberto & Mainardi, Francesco & Spada, Giorgio, 2017. "A generalization of the Lomnitz logarithmic creep law via Hadamard fractional calculus," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 333-338.
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    1. Long, Le Dinh & Zaky, Mahmoud A. & Luc, Nguyen Hoang & Moghaddam, B. Parsa, 2026. "Multi-operator iterative regularization framework for caputo-Hadamard fractional diffusion with environmental applications," Chaos, Solitons & Fractals, Elsevier, vol. 202(P2).

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