A boundary-value problem for the equation of mixed type with generalized operators of fractional differentiation in the boundary conditions
-
Oleg A. Repin
and
Svetlana K. Kumykova
Abstract
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.
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© 2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- Admissible pair of spaces for non-correctly solvable linear differential equations
- Defective functions of meromorphic functions in the unit disc
- A boundary-value problem for the equation of mixed type with generalized operators of fractional differentiation in the boundary conditions
- Density not realizable as the Jacobian determinant of a bilipschitz map
- An inequality involving the gamma and digamma functions
- Asymptotic behaviour of solutions to one-dimensional reaction diffusion cooperative systems involving infinitesimal generators
- Generalized slow growth of special monogenic functions
- Iterative algorithm for the split equality problem in Hilbert spaces
- On norm of single layer potentials on segments
Articles in the same Issue
- Frontmatter
- Admissible pair of spaces for non-correctly solvable linear differential equations
- Defective functions of meromorphic functions in the unit disc
- A boundary-value problem for the equation of mixed type with generalized operators of fractional differentiation in the boundary conditions
- Density not realizable as the Jacobian determinant of a bilipschitz map
- An inequality involving the gamma and digamma functions
- Asymptotic behaviour of solutions to one-dimensional reaction diffusion cooperative systems involving infinitesimal generators
- Generalized slow growth of special monogenic functions
- Iterative algorithm for the split equality problem in Hilbert spaces
- On norm of single layer potentials on segments
