AN INTERNAL BOUNDARY VALUE PROBLEM WITH THE RIEMANN-LIOUVILLE OPERATOR FOR THE MIXED TYPE EQUATION OF THE THIRD ORDER

被引：0

作者：

Repin, O. A. ^{[1
,2
]}

Kumykova, S. K. ^{[3
]}

机构：

[1] Samara State Econ Univ, Dept Math Stat & Econometr, 141 Sovetskoy Armii St, Samara 443090, Russia

[2] Samara State Tech Univ, Dept Appl Math & Comp Sci, 244 Molodogvardeyskaya St, Samara 443100, Russia

[3] Kabardino Balkarian State Univ, Dept Math Anal & Theory Funct, 173 Chernyshevskogo St, Nalchik 360004, Russia

来源：

VESTNIK SAMARSKOGO GOSUDARSTVENNOGO TEKHNICHESKOGO UNIVERSITETA-SERIYA-FIZIKO-MATEMATICHESKIYE NAUKI | 2016年 / 20卷 / 01期

关键词：

mixed type equation; Fredholm equation; Cauchy problem; fractional operators in the sense of Riemann-Liouville integro-differentiation;

D O I：

10.14498/vsgtu1461

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The unique solvability of the internal boundary value problem is investigated for the mixed type equation of the third order with Riemann-Liouville operators in boundary condition. The uniqueness theorem is proved for the different orders of operators of fractional integro-differentiation when the inequality constraints on the known functions exist. The existence of solution is verified by the method of reduction to Fredholm equations of the second kind, which unconditional solvability follows from the uniqueness of the solution of the problem.

引用

页码：43 / 53

页数：11

共 50 条

[31] Solution of an Initial Boundary Value Problem for a Multidimensional Fourth-Order Equation Containing the Bessel Operator
Karimov, Shakhobiddin
Tulasheva, Yorkinoy
MATHEMATICS, 2024, 12 (16)
[32] Boundary-Value Problem With Saigo Operators for Mixed Type Equation With Fractional Derivative
Repin, O. A.
RUSSIAN MATHEMATICS, 2018, 62 (01) : 70 - 75
[33] A boundary-value problem for the equation of mixed type with generalized operators of fractional differentiation in the boundary conditions
Repin, Oleg A.
Kumykova, Svetlana K.
JOURNAL OF APPLIED ANALYSIS, 2016, 22 (01) : 27 - 36
[34] A Nonlocal Problem for a Mixed-Type Equation Whose Order Degenerates Along the Line of Change of Type
Repin, O. A.
Kumykova, S. K.
RUSSIAN MATHEMATICS, 2013, 57 (08) : 49 - 56
[35] Boundary value problem for an advanced-retarded equation of mixed type with a nonsmooth degeneration line
A. N. Zarubin
Differential Equations, 2014, 50 : 1352 - 1363
[36] Boundary value problem for an advanced-retarded equation of mixed type with a nonsmooth degeneration line
Zarubin, A. N.
DIFFERENTIAL EQUATIONS, 2014, 50 (10) : 1352 - 1363
[37] The nonlocal problem for a non-stationary third order composite type equation with general boundary condition
Khashimov, A. R.
VESTNIK SAMARSKOGO GOSUDARSTVENNOGO TEKHNICHESKOGO UNIVERSITETA-SERIYA-FIZIKO-MATEMATICHESKIYE NAUKI, 2020, 24 (01): : 187 - 198
[38] Solution of the Mixed Problem for a Third-Order Partial Differential Equation
V. I. Uskov
Mathematical Notes, 2022, 111 : 932 - 939
[39] Nonlocal Tricomi boundary value problem for a mixed-type differential-difference equation
Zarubin, A. N.
VESTNIK SAMARSKOGO GOSUDARSTVENNOGO TEKHNICHESKOGO UNIVERSITETA-SERIYA-FIZIKO-MATEMATICHESKIYE NAUKI, 2021, 25 (01): : 35 - 50
[40] Solution of the Mixed Problem for a Third-Order Partial Differential Equation
Uskov, V., I
MATHEMATICAL NOTES, 2022, 111 (5-6) : 932 - 939

← 1 2 3 4 5 →