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A boundary-value problem for the equation of mixed type with generalized operators of fractional differentiation in the boundary conditions

Repin O. A., Kumykova S. K.

Journal of Applied Analysis

2016

Vol. 22, nr 1

27--36

The paper is devoted to the study of a boundary-value problem for an equation of mixed type with generalized operators of fractional differentiation in boundary conditions. We prove uniqueness of solutions under some restrictions on the known functions and on the different orders of the operators of generalized fractional differentiation appearing in the boundary conditions. Existence of solutions is proved by reduction to a Fredholm equation of the second kind, for which solvability follows from the uniqueness of the solution of our original problem.