## Abstract

In this work, we study an inverse problem to determine an unknown source term for fractional diffusion equation with Riemann–Liouville derivative. In general, the problem is severely ill posed in the sense of Hadamard. To regularize the unstable solution of the problem, we have applied the quasi-boundary value method. In the theoretical result, we show the error estimate between the exact solution and regularized solution with a priori parameter choice rules and analyze it. Eventually, a numerical example has been carried out, the result shows that our regularization method is converged.

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## Acknowledgements

This research was supported by the Macau Science and Technology Development Fund (Grant no. 0074/2019/A2) from the Macau Special Administrative Region of the P.R. China.

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Communicated by José Tenreiro Machado.

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Tuan, N.H., Zhou, Y., Long, L.D. *et al.* Identifying inverse source for fractional diffusion equation with Riemann–Liouville derivative.
*Comp. Appl. Math.* **39, **75 (2020). https://doi.org/10.1007/s40314-020-1103-2

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### Keywords

- Fractional diffusion equation
- Inverse problem
- Regularization

### Mathmatics Subject Classification

- 35R11
- 35B65
- 26A33