| 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.
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