A Survey on Existence Results for Boundary Value Problems of Nonlinear Fractional Differential Equations and Inclusions

被引：746

作者：

Agarwal, Ravi P. ^{[1
]}

Benchohra, Mouffak ^{[2
]}

Hamani, Samira ^{[2
]}

机构：

[1] Florida Inst Technol, Dept Math Sci, Melbourne, FL 32901 USA

[2] Univ Djillali Liabes Sidi Bel Abbes, Math Lab, Sidi Bel Abbes 22000, Algeria

来源：

ACTA APPLICANDAE MATHEMATICAE | 2010年 / 109卷 / 03期

关键词：

Boundary value problem; Initial value problems; Differential equations and inclusions; Caputo fractional derivative; Fractional integral; Existence; Uniqueness; Impulses; Fixed point; Selection; Nonlocal conditions; Integral conditions; COMPLEX DYNAMICS; PREDATOR SYSTEM; ORDER; MODEL; PREY; UNIQUENESS; NETWORKS; MAPPINGS; THEOREMS;

D O I：

10.1007/s10440-008-9356-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this survey paper, we shall establish sufficient conditions for the existence and uniqueness of solutions for various classes of initial and boundary value problem for fractional differential equations and inclusions involving the Caputo fractional derivative. The both cases of convex and nonconvex valued right hand side are considered. The topological structure of the set of solutions is also considered.

引用

页码：973 / 1033

页数：61

共 50 条

[41] Existence Results on Nonlinear Fractional Differential Inclusions
Mohammadi, Hakimeh
BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, 2021, 39 (06): : 23 - 30
[42] NONLINEAR BOUNDARY VALUE PROBLEMS FOR DIFFERENTIAL INCLUSIONS WITH CAPUTO FRACTIONAL DERIVATIVE
Benchohra, Mouffak
Hamani, Samira
TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2008, 32 (01) : 115 - 130
[43] On the existence for parametric boundary value problems of a coupled system of nonlinear fractional hybrid differential equations
Zhao, Yige
Sun, Yibing
TURKISH JOURNAL OF MATHEMATICS, 2022, 46 (01) : 612 - 625
[44] Existence of multiple positive solutions for singular boundary value problems of nonlinear fractional differential equations
Zhou, Wen-Xue
Zhang, Jian-Gang
Li, Jie-Mei
ADVANCES IN DIFFERENCE EQUATIONS, 2014,
[45] Existence of positive solution to the boundary value problems for coupled system of nonlinear fractional differential equations
Asaduzzaman, Md
Ali, Md Zulfikar
AIMS MATHEMATICS, 2019, 4 (03): : 880 - 895
[46] Existence of multiple positive solutions for singular boundary value problems of nonlinear fractional differential equations
Wen-Xue Zhou
Jian-Gang Zhang
Jie-Mei Li
Advances in Difference Equations, 2014
[47] Solvability of boundary value problems of nonlinear fractional differential equations
Weiqi Chen
Yige Zhao
Advances in Difference Equations, 2015
[48] A note on the existence of solutions for some boundary value problems of fractional differential inclusions
Cernea, Aurelian
FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2012, 15 (02) : 183 - 194
[49] Existence and approximation of solutions to nonlocal boundary value problems for fractional differential inclusions
Kamenskii M.
Obukhovskii V.
Petrosyan G.
Yao J.-C.
Fixed Point Theory and Applications, 2019 (1)
[50] Solvability of boundary value problems of nonlinear fractional differential equations
Chen, Weiqi
Zhao, Yige
ADVANCES IN DIFFERENCE EQUATIONS, 2015, : 1 - 13

← 1 2 3 4 5 →