Kernel determination problem in the fractional pseudo-integro-differential equation

In this work, we study direct-initial boundary value and inverse-kernel determination problems for one-dimensional time-fractional pseudo-diffusion equation of the third order. The unique solvability of the direct problem is investigated and a priori estimates for its solution are obtained in weighted spaces, which will be useful for studying the inverse problem. Further the inverse problem is equivalently reduced to a nonlinear integral equation. To prove the unique solvability of this equation. The fixed point principle is used to prove the unique solvability of this equation.