Solvability of a non-local problem with integral gluing condition for mixed type equation with Erdelyi-Kober operators

In this paper the existence and the uniqueness of solution of non-local problem with integral gluing condition for mixed type equation are investigated. Considering loaded parabolichyperbolic equation involve the Caputo fractional derivative and Erdelyi-Kober integrals. The uniqueness of solution is proved by the method of integral energy and the existence is proved by the method of integral equations.

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