An inverse problem to determine a space-dependent factor in a semilinear timefractional diffusion equation is considered. Additional data are given in the form of an integral with the Borel measure over the time. Uniqueness of the solution of the inverse problem is studied. The method uses a positivity principle of the corresponding differential equation that is also proved in the paper.

An inverse problem to determine a kernel in an evolutionary integral equation occurring in modeling of subdiffusion is considered. The existence, uniqueness and stability of a solution of the inverse problem are proved in an abstract setting. The results are global in time.

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The identification of a source term in a parabolic integro-differential equation is considered. We study the existence of the quasi-solution to this problem, Tikhonov regularization and a related gradient method.

We deduce formulas for the Fréchet derivatives of cost functionals of several inverse problems for a parabolic integrodifferential equation in a weak formulation. The method consists in the application of an integrated convolutional form of the weak problem and all computations are implemented in regular Sobolev spaces.