Inverse Problems for the Loaded Parabolic-Hyperbolic Equation Involves Riemann–Liouville Operator

In this article, the existence and the uniqueness of solution of inverse problems with non-linear gluing condition for the loaded parabolic-hyperbolic type equation is studied. The problem is reduced to study nonlinear Fredholm integral equation of second kind. The theorem on existence and uniqueness of solution was proved by the method of successive approximations.