Reconstruction of a space-dependent source in the inexact order time-fractional diffusion equation

Dang Duc Trong, Dinh Nguyen Duy Hai and Nguyen Dang Minh

Chaos, Solitons & Fractals, 2020, vol. 134, issue C

Abstract: An inverse problem to recover a space-dependent factor of a source term in the inexact order time-fractional diffusion equation from final data is considered. The problem arises in many applications, but it is in general ill-posed. The ill-posedness is since small errors in the input data cause large errors in the output solution. To overcome this instability we propose the stable approximation solution via a general modified quasi-boundary value regularization method. Order optimal convergence rates for the worst case error of the method are derived under the usual source condition by using an a-priori and an a-posteriori regularization parameter choice rules, respectively. Finally, several numerical examples are provided to illustrate the effectiveness of the proposed method.

Keywords: Inverse source problem; Time-fractional diffusion equation; Ill-posed problem; Regularization; Order optimal error bounds (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:134:y:2020:i:c:s0960077920301260

DOI: 10.1016/j.chaos.2020.109724

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