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

被引：1

作者：

Repin, Oleg A. ^{[1
]}

Kumykova, Svetlana K. ^{[2
]}

机构：

[1] Samara State Econ Univ, Soviet Army Str 141, Samara 443090, Russia

[2] Kabardino Balkarian State Univ, Chernyshevsky Str 173, Nalchik 360004, Russia

来源：

JOURNAL OF APPLIED ANALYSIS | 2016年 / 22卷 / 01期

关键词：

Boundary-value problem; operator of fractional integration; operator of fractional differentiation; Fredholm equation; singular integral equation; regularization;

D O I：

10.1515/jaa-2016-0003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：27 / 36

页数：10