On an inverse problem for a nonlinear loaded parabolic-hyperbolic equation of fractional order

The work is devoted to the study of the unique solvability of an inverse problem for a nonlinear parabolic-hyperbolic equation with the Caputo fractional derivative and nonlinear loads. The inverse problem is well posed in the mixed domain with characteristic triangle on the hyperbolic part. With the aid of main functional relations and nonlinear gluing condition, the investigation of the problem is reduced to a nonlinear integral equation. The unique solvability of the integral equation is proven by the method of successive approximations.