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

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

Chaos, Solitons & Fractals, 2025, vol. 201, issue P2

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.

Keywords: Inverse random source problem; Caputo–Hadamard type; Fractional Brownian motion; Stochastic time-fractional diffusion equation; Iterative fractional Tikhonov–Landweber method (search for similar items in EconPapers)
Date: 2025
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:201:y:2025:i:p2:s0960077925012469

DOI: 10.1016/j.chaos.2025.117233

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