Solution to Fractional Integro-differential Equation with Unknown Flux on the Dirichlet Boundary
DOI:
https://doi.org/10.5890/DNC.2022.12.010Abstract
In this article, we prove the existence, uniqueness and some stability results for fractional integro-differential equation of reconstruction of the unknown time-dependent boundary function $\gamma \left( t\right) $ from an additional integral measurement $\theta \left( t\right) =\int_{\Omega }I^{1-\alpha }\left( u\left( t, x\right) \right) dx$ by the use of Rothe time discretization. Numerical experiments are given to illustrate the results.References
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