Existence for fractional Dirichlet boundary value problem under barrier strip conditions
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Authors
Qilin Song
- College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 266590, P. R. China.
Xiaooyu Dong
- College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 266590, P. R. China.
Zhanbing Bai
- College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 266590, P. R. China.
Bo Chen
- College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, P. R. China.
Abstract
In this paper, a fixed-point theorem is used to establish existence results for fractional Dirichlet boundary value problem
\[D^\alpha x(t)=f(t,x(t),D^{\alpha-1}x(t)),\quad x(0)=A,\quad x(1)=B\]
where \(1 < \alpha\leq 2,D^\alpha x(t)\) is the conformable fractional derivative, and \(f : [0, 1] \times R^2 \rightarrow R\) is a continuous function. The main
condition is sign condition. The method used is based upon the theory of fixed-point index.
Share and Cite
ISRP Style
Qilin Song, Xiaooyu Dong, Zhanbing Bai, Bo Chen, Existence for fractional Dirichlet boundary value problem under barrier strip conditions, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 7, 3592--3598
AMA Style
Song Qilin, Dong Xiaooyu, Bai Zhanbing, Chen Bo, Existence for fractional Dirichlet boundary value problem under barrier strip conditions. J. Nonlinear Sci. Appl. (2017); 10(7):3592--3598
Chicago/Turabian Style
Song, Qilin, Dong, Xiaooyu, Bai, Zhanbing, Chen, Bo. "Existence for fractional Dirichlet boundary value problem under barrier strip conditions." Journal of Nonlinear Sciences and Applications, 10, no. 7 (2017): 3592--3598
Keywords
- Barrier strips
- fixed-point index
- conformable fractional derivative.
MSC
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