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Regularization of inverse source problem for fractional diffusion equation with Riemann–Liouville derivative

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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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Authors and Affiliations

  1. School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao, 066004, China

    Songshu Liu & Fuquan Sun

  2. School of Mathematical Sciences, Heilongjiang University, Harbin, 150080, China

    Lixin Feng

Authors
  1. Songshu Liu
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  2. Fuquan Sun
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  3. Lixin Feng
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Correspondence to Lixin Feng.

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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

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