A non-local problem with discontinuous matching condition for loaded mixed type equation involving the Caputo fractional derivative
Kishin SadaranganiUniversity of Las-Palmas de Gran Canaria, Las Palmas, SpainObidjon Khayrullayevich AbdullaevNational University of Uzbekistan, Tashkent, Uzbekistan
ABI
Abstract
This research work is devoted to investigations of the existence and uniqueness of the solution of a non-local boundary value problem with discontinuous matching condition for the loaded equation. Considering parabolic-hyperbolic type equations involves the Caputo fractional derivative and loaded part joins in Riemann-Liouville integrals. The uniqueness of a solution is proved by the method of integral energy and the existence is proved by the method of integral equations.