Abstract
In this paper, we consider an inverse source problem for fractional diffusion equation with Riemann–Liouville derivative. The considered problem is ill-posed, i.e., the solution does not depend continuously on the given data. We assume the solutions of the equation can be represented by a Fourier series. The Tikhonov regularization method is applied to solve this problem. In the theoretical results, the convergence estimates between the exact solutions and the regularized solutions are presented under a priori and a posteriori parameter choice rules.
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Communicated by José Tenreiro Machado.
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S. Liu was supported by Fundamental Research Funds of the Central Universities (N182304024). L. Feng was supported by National Natural Science Foundation of China (11871198).
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Liu, S., Sun, F. & Feng, L. Regularization of inverse source problem for fractional diffusion equation with Riemann–Liouville derivative. Comp. Appl. Math. 40, 112 (2021). https://doi.org/10.1007/s40314-021-01438-1
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DOI: https://doi.org/10.1007/s40314-021-01438-1
Keywords
- Fractional diffusion equation
- Inverse source problem
- Ill-posed problem
- Regularization method
- Convergence estimates