The Inverse Problem for the Abstract Diffusion Equation with a Fractional Derivative

The inverse problem of determining the coefficient of an abstract fractional diffusion equation is considered. First, conditions under which the direct problem is well posed are investigated and the equivalence of the inverse problem to a certain integral equation is proved. Then the properties of solutions to the direct problem are used to study the inverse problem. Results on the local existence, uniqueness, and stability of the solution to the inverse problem are obtained by using a fixed point theorem in an appropriate Banach space.

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