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The Inverse Problem for a Mixed Type Equation with a Fractional Order Operator in a Rectangular Domain

Russian Mathematics, ISSN: 1934-810X, Vol: 65, Issue: 3, Page: 25-42
2021
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Article Description

We study the inverse problem for a mixed type equation with the Riemann–Liouville and Caputo operator in arectangular domain. A criterion for the uniqueness and existenceof a solution to the inverse problem is established. The solutionto the problem is constructed in the form of the sum of a seriesof eigenfunctions of the corresponding one-dimensional spectralproblem. It is proved that the unique solvability of the inverseproblem substantially depends on the choice of the boundary of arectangular region. An example is constructed, in which the inverseproblem with homogeneous conditions has a nontrivial solution.Estimates are obtained that allow substantiating the convergenceof series in the class of regular solutions of this equation andthe stability of the solution of the inverse problem on boundarydata.

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