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Identifying inverse source for fractional diffusion equation with Riemann-Liouville derivative. (English) Zbl 1449.35450

Summary: 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.

MSC:

35R11 Fractional partial differential equations
35B65 Smoothness and regularity of solutions to PDEs
26A33 Fractional derivatives and integrals

Software:

mlf; Mittag-Leffler
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Full Text: DOI

References:

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