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<p>The current paper is devoted to the sideways problem for the nonlinear multi-term time-fractional diffusion equation. The investigated problem consists of the recovering of the diffusion distribution from the boundary data. Unlike previous works, the reaction term in this paper is allowed to be a locally Lipschitz function. By using the Banach fixed point theorem and some appropriate estimates, we show that the investigated problem is ill-posed. We further propose a fractional Tikhonov method written in the form of a nonlinear integral equation to regularize the problem. The Hölder convergence rates are obtained under some regularity assumptions on the solution. Two numerical examples with support from the Fast Fourier Transform are provided to illustrate the results.</p>

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Determination of the diffusion distribution for the nonlinear multi-term time-fractional diffusion equation

  • 期刊论文

  • 发表日期：

    2026年5月2日

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  • Tran Thi Khieu

摘要

The current paper is devoted to the sideways problem for the nonlinear multi-term time-fractional diffusion equation. The investigated problem consists of the recovering of the diffusion distribution from the boundary data. Unlike previous works, the reaction term in this paper is allowed to be a locally Lipschitz function. By using the Banach fixed point theorem and some appropriate estimates, we show that the investigated problem is ill-posed. We further propose a fractional Tikhonov method written in the form of a nonlinear integral equation to regularize the problem. The Hölder convergence rates are obtained under some regularity assumptions on the solution. Two numerical examples with support from the Fast Fourier Transform are provided to illustrate the results.