On a boundary-value problem with sewing condition of integral form for parabolic-hyperbolic equation with fractional derivative

Subject Fractional differential equations and applications
Title On a boundary-value problem with sewing condition of integral form for parabolic-hyperbolic equation with fractional derivative
Author(s) Berdyshev A.S.; Karimov E.T.; Akhtaeva N.S.
Keywords parabolic-hyperbolic equation; Caputo fractional differential operator
Abstract In this study, we consider a boundary problem with sewing condition of integral form for mixed parabolic-hyperbolic type equation with the Caputo fractional derivative. The uniqueness of the solution for considered problem we prove by the method of energy integrals. The existence of the solution have been proved by reducing the considered problem to the Fredholm integral equation. We represent solution in an explicit form using Green's function.