Subject 
Fractional differential equations and applications 
Title 
On a boundaryvalue problem with sewing condition of integral form for parabolichyperbolic equation with fractional derivative 
Author(s) 
Berdyshev A.S.; Karimov E.T.; Akhtaeva N.S. 
Keywords 
parabolichyperbolic equation; Caputo fractional differential operator 
Abstract 
In this study, we consider a boundary problem with sewing condition of integral form for mixed parabolichyperbolic 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.
