Computational Mathematics and Modeling

, Volume 30, Issue 4, pp 340–351

# Stabilized Solution for a Time-Fractional Inverse Problem with an Unknown Nonlinear Condition

Article

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.

## Keywords

Time fractional inverse problem Caputo fractional derivative Mollification Finite difference scheme Convergence analysis

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