Recovering a Space-Dependent Source Term in the Fractional Diffusion Equation with the Riemann–Liouville Derivative

Songshu Liu ()
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Songshu Liu: School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China

Mathematics, 2022, vol. 10, issue 17, 1-13

Abstract: This research determines an unknown source term in the fractional diffusion equation with the Riemann–Liouville derivative. This problem is ill-posed. Conditional stability for the inverse source problem can be given. Further, a fractional Tikhonov regularization method was applied to regularize the inverse source problem. In the theoretical results, we propose a priori and a posteriori regularization parameter choice rules and obtain the convergence estimates.

Keywords: inverse problem; fractional diffusion equation with Riemann–Liouville derivative; ill-posed problem; fractional Tikhonov regularization method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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