INTEGRAL CONDITION FOR BENNEY-LUKE TYPE EQUATION THE PROBLEM GIVEN WITH THE RIGHT AND INVERSE PROBLEM

The article studies the fractional order equation of the form where , for the time interval with the integral boundary condition Here, is a self-adjoint, unbounded, positive operator defined on a separable Hilbert space , and is a compact operator. The article demonstrates the existence and uniqueness of solutions to the problem using the Fourier method. Additionally, it addresses the inverse problem concerning the determination of the right-hand side of the equation.