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An inverse source problem for a two parameter anomalous diffusion equation with nonlocal boundary conditions. (English) Zbl 1386.35479
Summary: We consider the inverse problem of determination of the solution and a source term for a time fractional diffusion equation in two dimensional space. The time fractional derivative is the Hilfer derivative. A bi-orthogonal system of functions in $$L^2(\Omega)$$, obtained from the associated non-self-adjoint spectral problem and its adjoint problem, is used to prove the existence and uniqueness of the solution of the inverse problem. The stability of the solution of the inverse problem on the given data is proved.

##### MSC:
 35R30 Inverse problems for PDEs 35R11 Fractional partial differential equations 65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
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