Inverse Boundary Value Problem for Two-Dimensional Pseudo Parabolic Equation of Time-Fractional Order with Additional Integral Condition

Inverse boundary value problem for two-dimensional pseudo parabolic equation of third order with additional integral condition is considered.We first reduce our problem to some equivalent (in some sense) one.Using the Fourier method, the equivalent problem, in turn, is reduced to the system of integral equations.Then, using contraction mapping method, we prove the existence and uniqueness for the solution of the system of integral equations, which is also a unique solution of the equivalent problem.Finally, using equivalence, we prove the existence and uniqueness for the classical solution of the original problem.