An Inverse Problem of Determining the Kernel of a Fractional Pseudo-Integro-Differential Equation

In this work, the kernel determination inverse problem with initial-boundary and over-determination conditions for a pseudoparabolic integrodifferential equation involving fractional Caputo derivative is studied. First, an equivalent auxiliary problem is reduced. Investigation of the direct problem is conducted by the Fourier method. The inverse problem reduces to solving a Volterra type integral equation of the second kind with respect to an unknown function. Using the fixed point theorem, the unique solvability of the inverse problem is proven for a sufficiently small segment.