Stabilized Solution for a Time-Fractional Inverse Problem with an Unknown Nonlinear Condition
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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.
KeywordsTime fractional inverse problem Caputo fractional derivative Mollification Finite difference scheme Convergence analysis
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