On a problem for the loaded degenerating mixed type equation involving integral-differential operators

This work aims to study the existence and uniqueness of a solution for a problem of the loaded degenerating mixed type equation. We consider the loaded parabolic-hyperbolic equation involving the Caputo fractional derivative and Riemann–Liouville integrals. The uniqueness of solution is proved by using the method of integral energy applying an extremum principle. Based on the statement of equivalence between “The existence and uniqueness of solution” and “Solvability of the respectively Fredholm type integral equations”, the existence of a solution was proved.