BOUNDARY VALUE PROBLEMS FOR DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER

被引：0
|
作者：
Aleroev, T. S. [1 ,2 ]
Aleroeva, H. T. [3 ]
Nie, Ning-Ming [4 ,5 ]
Tang, Yi-Fa [4 ]
机构：
[1] Moscow Inst Municipal Serv & Construct, Fac Higher Math, Moscow, Russia
[2] Acad Natl Econ Govt Russian Federat, Moscow 119571, Russia
[3] Moscow Tech Univ Commun & Informat, Moscow 111024, Russia
[4] Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
[5] Chinese Acad Sci, Grad Sch, Beijing 100190, Peoples R China
来源：
MEMOIRS ON DIFFERENTIAL EQUATIONS AND MATHEMATICAL PHYSICS | 2010年 / 49卷
关键词：
Caputo's derivatives; Riemann Liouville derivatives; fractional differential equation; two-point boundary value problem; existence and uniqueness; single shooting method;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We carry out spectral analysis of a class of integral operators associated with fractional order differential equations arising in mechanics. We establish a connection between the eigenvalues of these operators and the zeros of Mittag Leffler type functions. We give sufficient conditions for complete nonselfadjointness and completeness of the systems of the eigenfunctions. We prove the existence and uniqueness of solutions for several kinds of two-point boundary value problems for fractional differential equations with Caputo or Riemann Liouville derivatives, and design single shooting methods to solve them numerically.
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页码：21 / 82
页数：62
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