Inverse Problem for a Third-Order Parabolic-Hyperbolic Equation Involves Fractional Derivatives

In this article the questions of unique solvability of inverse problem for a third order parabolic-hyperbolic type equation with Caputo derivatives are considered. Inverse problem is studied by an additional boundary condition on the hyperbolic domain and integral gluing condition on the line $$y=0$$ . The problem is reduced to study a second kind Volterra type integral equation with a shift. Existence and uniqueness of solution are proved by the method of successive approximations of factorial law.

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