• 论文 •

### 一个新的分数阶微分方程边值问题正解的存在性结果

1. 1. 中国石油大学(华东)理学院计算与应用数学系,青岛 266555; 东北师范大学数学与统计学院,长春 130024;  2.新疆伊犁师范学院数学与统计学院,应用数学研究所,伊宁 835000
• 出版日期:2012-05-25 发布日期:2012-08-22

XU Xiaojie, HU Weimin. A NEW EXISTENCE RESULT OF POSITIVE SOLUTIONS FOR A ClASS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION BOUNDARY VALUE  ROBLEMS[J]. Journal of Systems Science and Mathematical Sciences, 2012, 32(5): 580-590.

### A NEW EXISTENCE RESULT OF POSITIVE SOLUTIONS FOR A ClASS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION BOUNDARY VALUE  ROBLEMS

XU Xiaojie1, HU Weimin2

1. 1. School of School of Science, Department of Mathematics and Computational Science,China University of Petroleum (East China), Qingdao 266555;School of Mathematics and Statistics, Northeast Normal University, Changchun 130024; 2. School of Mathematics and Statistics, Institute of Applied Mathematics, Ili Normal University,Yining 835000
• Online:2012-05-25 Published:2012-08-22

In this paper, we consider the existence and uniqueness of positive solutions for a nonlinear fractional differential equation boundary-value problem D 0+u(t) = f(t, u(t)), 0 < t < 1,
u(0) = u(1) = u′(0) = u′(1) = 0,
where 3 < ≤ 4, and D 0+ is the standard Riemann-Liouville differentiation, and f : [0, 1] ×[0,∞) → [0,∞) is continuous. Firstly, the uniqueness of positive solution is obtained by useof contraction map principle. Then, some existence results of positive solutions are obtained.The proofs are based upon the reduction of the problem considered to the equivalent Fredholm integral equation of second kind.

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