Boundary Value Problem for the Time-Fractional Telegraph Equation with Caputo Derivatives

被引：10
|
作者：
Mamchuev, M. O. [1 ]
机构：
[1] Inst Appl Math & Automat KBSC RAS, Shortanov Str,89 A, Nalchik 360000, Russia
来源：
MATHEMATICAL MODELLING OF NATURAL PHENOMENA | 2017年 / 12卷 / 03期
关键词：
Green function method; Caputo derivative; fractional telegraph equation; general representation of solution; boundary value problems; Green functions; 2ND-ORDER PARABOLIC EQUATION; DIFFUSION EQUATION;
D O I：
10.1051/mmnp/201712308
中图分类号：
Q [生物科学];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
In this paper the Green formula for the operator of fractional differentiation in Caputo sense is proved. By using this formula the integral representation of all regular in a rectangular domains solutions is obtained in the form of the Green formula for operator generating the time-fractional telegraph equation. The unique solutions of the initial-boundary value problem with boundary conditions of first kind is constructed. The proposed approach can be used to study the more general evolution FPDE as well as ODE with Caputo derivatives.
引用
收藏
页码：82 / 94
页数：13
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