In this paper, we consider a time-fractional inverse problem in which the nonlinear boundary conditions contain an unknown function. A finite difference scheme will be proposed to solve numerically the inverse problem. This inverse problem is generally ill-posed. For this reason, we will employ the mollification regularization method with the generalized cross-validation criterion to find a stable solution. The stability and convergence of numerical solutions are investigated. Finally, some numerical examples are presented to illustrate the validity and effectiveness of the proposed method.
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Babaei, A., Banihashemi, S. Stabilized Solution for a Time-Fractional Inverse Problem with an Unknown Nonlinear Condition. Comput Math Model 30, 340–351 (2019). https://doi.org/10.1007/s10598-019-09460-z
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DOI: https://doi.org/10.1007/s10598-019-09460-z