Boundary Value Problems for a Parabolic-Hyperbolic Equation with Nonlinear Loaded Terms

In the present work local and nonlocal boundary value problem involves nonlinear gluing condition for a loaded parabolic-hyperbolic type equation with parameter is considered. The parabolic part of this equation is fractional analog of heat equation and the hyperbolic part is the telegraph equation. In addition, each of equations involve nonlinear loaded terms. The considered problem for real values of the parameter is reduced to an equivalent nonlinear second kind Volterra integral equation. The existence and uniqueness of solution was proved by the successive approximations method.

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