Positive solutions for integral boundary value problem of two-term fractional differential equations

被引：23

作者：

Xu, Mengrui ^{[1
]}

Han, Zhenlai ^{[1
]}

机构：

[1] Univ Jinan, Sch Math Sci, Jinan, Shandong, Peoples R China

来源：

BOUNDARY VALUE PROBLEMS | 2018年

关键词：

Fractional differential equations; Boundary value problem; Positive solutions; UNIQUENESS; EXISTENCE;

D O I：

10.1186/s13661-018-1021-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate a class of nonlinear two-term fractional differential equations involving two fractional orders delta is an element of ( 1, 2] and tau is an element of( 0, d) with integral boundary value conditions. By the Schauder fixed point theorem we obtain the existence of positive solutions based on the method of upper and lower solutions. Then we obtain the uniqueness result by the Banach contraction mapping principle. Examples are given to illustrate our main results.

引用

页数：13

共 30 条

[11] Positive solutions for a system of nonlinear fractional nonlocal boundary value problems with parameters and p-Laplacian operator [J].

Hao, Xinan ;

Wang, Huaqing ;

Liu, Lishan ;

Cui, Yujun .

BOUNDARY VALUE PROBLEMS, 2017,

[12] Existence for boundary value problems of two-term Caputo fractional differential equations [J].

Ibrahim, Badawi Hamza Elbadawi ;

Dong, Qixiang ;

Fan, Zhenbin .

JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2017, 10 (02) :511-520

[13] Multiplicity of solutions for integral boundary value problems of fractional differential equations with upper and lower solutions [J].

Jia, Mei ;

Liu, Xiping .

APPLIED MATHEMATICS AND COMPUTATION, 2014, 232 :313-323

[14]

Kilbas A. A., 2006, Theory and applications of fractional differential equations, Vvol. 204

[15] Langevin equation with two fractional orders [J].

Lim, S. C. ;

Li, Ming ;

Teo, L. P. .

PHYSICS LETTERS A, 2008, 372 (42) :6309-6320

[16] The method of lower and upper solutions for the general boundary value problems of fractional differential equations with p-Laplacian [J].

Liu, Xiping ;

Jia, Mei .

ADVANCES IN DIFFERENCE EQUATIONS, 2018,

[17] The method of lower and upper solutions for mixed fractional four-point boundary value problem with p-Laplacian operator [J].

Liu, Xiping ;

Jia, Mei ;

Ge, Weigao .

APPLIED MATHEMATICS LETTERS, 2017, 65 :56-62

[18] Multiple solutions for fractional differential equations with nonlinear boundary conditions [J].

Liu, Xiping ;

Jia, Mei .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 59 (08) :2880-2886

[19] Fractional Langevin equation [J].

Lutz, E .

PHYSICAL REVIEW E, 2001, 64 (05) :4

[20]

Podlubny I., 1999, Fractional differential equations

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