Solvability of a Non-local Problem with Integral Transmitting Condition for Mixed Type Equation with Caputo Fractional Derivative

被引：45

作者：

Agarwal, Praveen ^{[1
]}

Berdyshev, Abdumauvlen ^{[2
]}

Karimov, Erkinjon ^{[3
]}

机构：

[1] Anand Int Coll Engn, Dept Math, Jaipur, Rajasthan, India

[2] Univ Named Abai, Kazakh Natl Pedag, Alma Ata, Kazakhstan

[3] Natl Univ Uzbekistan, Inst Math, Tashkent, Uzbekistan

来源：

RESULTS IN MATHEMATICS | 2017年 / 71卷 / 3-4期

关键词：

Caputo derivative; transmitting condition; parabolic-hyperbolic equation; Green's function; PARABOLIC-HYPERBOLIC EQUATION; BOUNDARY-VALUE PROBLEM;

D O I：

10.1007/s00025-016-0620-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the present paper, we discuss solvability questions of a non-local problem with integral form transmitting conditions for a mixed parabolic-hyperbolic type equation with the Caputo fractional derivative in a domain bounded by smooth curves. A uniqueness of the solution for a formulated problem we prove using energy integral method with some modifications. The existence of solution will be proved by equivalent reduction of the studied problem into a system of second kind Fredholm integral equations.

引用

页码：1235 / 1257

页数：23

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