Positive solutions for nonlinear fractional differential equations

被引：29

作者：

Boulares, Hamid ^{[1
]}

Ardjouni, Abdelouaheb ^{[2
,3
]}

Laskri, Yamina ^{[4
]}

机构：

[1] Guelma Univ, Depatement Math, Fac Sci, Guelma 24000, Algeria

[2] Univ Souk Ahras, Fac Sci & Technol, Dept Math & Informat, POB 1553, Souk Ahras 41000, Algeria

[3] Univ Annaba, Dept Math, Appl Math Lab, Fac Sci, POB 12, Annaba 23000, Algeria

[4] Univ Annaba, Depatement Math, Fac Sci, POB 12, Annaba 23000, Algeria

来源：

POSITIVITY | 2017年 / 21卷 / 03期

关键词：

Fractional differential equations; Positive solutions; Upper and lower solutions; Existence; Uniqueness; Fixed point theorems; BOUNDARY-VALUE PROBLEM; EXISTENCE;

D O I：

10.1007/s11117-016-0461-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the existence and uniqueness of positive solutions of the nonlinear fractional differential equation {D-C(alpha) x (t) = f (t, x(t)) + D-C(alpha-1) g (t, x (t)), 0 < t <= T, x (0) =theta(1) > 0, x' (0) =theta(2) > 0, where 1 < alpha <= 2. In the process we convert the given fractional differential equation into an equivalent integral equation. Then we construct appropriate mapping and employ Schauder fixed point theorem and the method of upper and lower solutions to show the existence of a positive solution of this equation. We also use the Banach fixed point theorem to show the existence of a unique positive solution. The results obtained here extend the work of Matar (AMUC 84(1):51-57, 2015 [7]). Finally, an example is given to illustrate our results.

引用

页码：1201 / 1212

页数：12

共 50 条

[41] Existence of multiple positive solutions for singular boundary value problems of nonlinear fractional differential equations [J].

Zhou, Wen-Xue ;

Zhang, Jian-Gang ;

Li, Jie-Mei .

ADVANCES IN DIFFERENCE EQUATIONS, 2014,

[42] Multiple positive solutions to systems of nonlinear semipositone fractional differential equations with coupled boundary conditions [J].

Yuan, Chengjun ;

Jiang, Daqing ;

O'Regan, Donal ;

Agarwal, Ravi P. .

ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2012, (13) :1-17

[43] Positive solutions for a coupled system of nonlinear differential equations of mixed fractional orders [J].

Zhao, Yige ;

Sun, Shurong ;

Han, Zhenlai ;

Feng, Wenquan .

ADVANCES IN DIFFERENCE EQUATIONS, 2011,

[44] On The Existence of Positive Solutions for Boundary Value Problems of Nonlinear Fractional Differential Equations [J].

Zhao, Yige ;

Sun, Shurong .

PROCEEDINGS OF THE 7TH CONFERENCE ON BIOLOGICAL DYNAMIC SYSTEM AND STABILITY OF DIFFERENTIAL EQUATION, VOLS I AND II, 2010, :682-685

[45] POSITIVE SOLUTIONS OF ARBITRARY ORDER NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH ADVANCED ARGUMENTS [J].

Ntouyas, Sotiris K. ;

Wang, Guotao ;

Zhang, Lihong .

OPUSCULA MATHEMATICA, 2011, 31 (03) :433-442

[46] Positive Solutions for System of Nonlinear Fractional Differential Equations in Two Dimensions with Delay [J].

Babakhani, Azizollah .

ABSTRACT AND APPLIED ANALYSIS, 2010, :1-16

[47] POSITIVE SOLUTIONS FOR INTEGRAL BOUNDARY VALUE PROBLEMS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS [J].

Chakuvinga, Tawanda gallan ;

Topal, Fatma serap .

MISKOLC MATHEMATICAL NOTES, 2024, 25 (01) :173-188

[48] Classifications and existence criteria for positive solutions of systems of nonlinear differential equations [J].

Li, WT ;

Yang, XJ .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2004, 298 (02) :446-462

[49] Positive solutions for a new class of Hadamard fractional differential equations on infinite intervals [J].

Li, Shunyong ;

Zhai, Chengbo .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2019, 2019 (1) :1-9

[50] Positive solutions for eigenvalue problems of fractional differential equations with p-Laplacian [J].

Lu, H. ;

Han, Z. ;

Sun, S. ;

Zhang, C. .

SCIENTIA IRANICA, 2015, 22 (03) :755-764

← 1 2 3 4 5 →