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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Solution to Fractional Integro-differential Equation with Unknown Flux on the Dirichlet Boundary

Discontinuity, Nonlinearity, and Complexity 11(4) (2022) 723--734 | DOI:10.5890/DNC.2022.12.010

Amel Labadla, Abderrazek Chaoui, Manal Djaghout

Department of Mathematics, Faculty of Sciences, University 8 May 1945, B.P.401, 24000, Guelma, Algeria

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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.


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