Some boundary value problems of fractional differential equations and inclusions

被引：50

作者：

Ahmad, Bashir ^{[1
]}

Nieto, Juan J. ^{[2
]}

Pimentel, Johnatan ^{[2
]}

机构：

[1] King Abdulaziz Univ, Dept Math, Fac Sci, Jeddah 21589, Saudi Arabia

[2] Univ Santiago de Compostela, Dept Anal Matemat, Fac Matemat, Santiago De Compostela 15782, Spain

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2011年 / 62卷 / 03期

关键词：

Fractional differential equations; Mixed and closed boundary conditions; Existence; Leray-Schauder theory; Fixed point theorems for multivalued maps; ASYMPTOTICS;

D O I：

10.1016/j.camwa.2011.02.035

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the existence of solutions for nonlinear fractional differential equations and inclusions of order q is an element of (1,2] with families of mixed and closed boundary conditions. In case of inclusion problems, the existence results are established for convex as well as nonconvex multivalued maps. Our results are based on Leray-Schauder degree theory, nonlinear alternative of Leray-Schauder type, and some fixed point theorems for multivalued maps. Some interesting special cases are also discussed. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：1238 / 1250

页数：13

共 15 条

[1] On the concept of solution for fractional differential equations with uncertainty [J].

Agarwal, Ravi P. ;

Lakshmikantham, V. ;

Nieto, Juan J. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (06) :2859-2862

[2] Existence of solutions for irregular boundary value problems of nonlinear fractional differential equations [J].

Ahmad, Bashir .

APPLIED MATHEMATICS LETTERS, 2010, 23 (04) :390-394

[3] Heat kernel asymptotics of Zaremba boundary value problem [J].

Avramidi, IG .

MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY, 2004, 7 (01) :9-46

[4] EXTENSIONS AND SELECTIONS OF MAPS WITH DECOMPOSABLE VALUES [J].

BRESSAN, A ;

COLOMBO, G .

STUDIA MATHEMATICA, 1988, 90 (01) :69-86

[5]

Castaing C., 1977, CONVEX ANAL MEASURAB, V580, DOI DOI 10.1007/BFB0087686

[6] MULTI-VALUED CONTRACTION MAPPINGS IN GENERALIZED METRIC SPACES [J].

COVITZ, H ;

NADLER, SB .

ISRAEL JOURNAL OF MATHEMATICS, 1970, 8 (01) :5-&

[7] On initial and boundary value problems for fractional order mixed type functional differential inclusions [J].

Darwish, Mohamed Abdalla ;

Ntouyas, S. K. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 59 (03) :1253-1265

[8]

Deimling K., 1992, de Gruyter Ser. Nonlinear Anal. Appl, DOI DOI 10.1515/9783110874228

[9]

DUGUNDJI J, 2005, FIXED POINT THEORY

[10]

Hu S., 1997, Handbook of multivalued analysis, DOI 10.1007/978-1-4615-6359-4

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