A Nonlocal Problem with an Integral Matching Condition for a Loaded Parabolic-Hyperbolic Equation with a Fractional Caputo Derivative

A nonlocal problem with an integral matching condition is studied for a parabolic-hyperbolic equation with two lines of type change containing a nonlinear loaded term. The uniqueness of the solution of the problem is proved by the method of energy integrals and the existence, using the theory of integral equations. Classes and sufficient conditions are determined for given functions that ensure the unique solvability of the problem under study.

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