Unique solvability of a non-local problem for mixed-type equation with fractional derivative

被引：5
作者：
Karimov, Erkinjon T. [1 ,2 ]
Berdyshev, Abdumauvlen S. [3 ]
Rakhmatullaeva, Nilufar A. [4 ]
机构：
[1] Sultan Qaboos Univ, Dept Math & Stat, Muscat 123, Oman
[2] Natl Univ Uzbekistan, Inst Math, Durmon Yuli 29, Tashkent 100125, Uzbekistan
[3] Kazakh Natl Pedag Univ, Alma Ata, Kazakhstan
[4] Tashkent State Tech Univ, Univ Str 2, Tashkent 100095, Uzbekistan
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2017年 / 40卷 / 08期
关键词：
Caputo fractional derivative; mixed-type equation; Volterra integral equation; parabolic-hyperbolic-type equation; Green's function; PARABOLIC-HYPERBOLIC EQUATION; BOUNDARY-VALUE PROBLEM;
D O I：
10.1002/mma.4215
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this work, we investigate a boundary problem with non-local conditions for mixed parabolic-hyperbolic-type equation with three lines of type changing with Caputo fractional derivative in the parabolic part. We equivalently reduce considered problem to the system of second kind Volterra integral equations. In the parabolic part, we use solution of the first boundary problem with appropriate Green's function, and in hyperbolic parts, we use corresponding solutions of the Cauchy problem. Copyright (c) 2016 John Wiley & Sons, Ltd.
引用
收藏
页码：2994 / 2999
页数：6
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