On a Boundary Value Problem for a Third-Order Equation of Parabolic-Hyperbolic Type with a Fractional Order Operator

被引：0

作者：

Kadirkulov, B. J. ^{[1
]}

Jalilov, M. A. ^{[2
]}

机构：

[1] Tashkent State Univ Oriental Studies, Dept Math & Informat Technol, Tashkent 100060, Uzbekistan

[2] Ferghana State Univ, Ferghana 150100, Uzbekistan

来源：

LOBACHEVSKII JOURNAL OF MATHEMATICS | 2023年 / 44卷 / 07期

关键词：

parabolic-hyperbolic equation; Gerasimov-Caputo differential operator; integral equation; uniqueness of a solution; existence of a solution; the Green function; Volterra integral equation; UNIQUE SOLVABILITY; MIXED-TYPE;

D O I：

10.1134/S1995080223070223

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the paper, we consider a boundary value problem for a third-order mixed differential equation of parabolic-hyperbolic type with a fractional Gerasimov- Caputo operator. Under certain conditions on the data of a problem, applying the methods of the theory of integral equations and the Green function, we prove the unique solvability of the problem. The uniqueness of the solution is proved by the method of the extremum principle, and the existence of this problem is proved by reducing it to a boundary value problem for a fractional order differential equation, as well as to the Volterra integral equation of the second kind.

引用

页码：2725 / 2737

页数：13

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