# POSITIVE SOLUTIONS FOR BOUNDARY VALUE PROBLEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION

Volume 1, Issue 3, pp 123-131
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### Authors

TINGTING QIU - Department of Mathematics, Shandong University of Science and Technology,Qingdao, 266510, PRC.. ZHANBING BAI - Department of Mathematics, Shandong University of Science and Technology, Qingdao, 266510, PRC..

### Abstract

We investigate the positive solution of nonlinear fractional differential equation with semi-positive nonlinearity $\begin{cases} D^\alpha_{0^+}u(t) + f(t, u(t)) = 0,\,\,\,\,\, 0 < t < 1,\\ u(0) = u'(1) = u''(0) = 0 \end{cases}$ where $2 < \alpha\leq 3$ is a real number, $D^\alpha_{0^+}$ is the Caputo's differentiation, and $f : [0; 1] \times [0, \infty) \rightarrow (-\infty , \infty)$. By use of Krasnosel'skii fixed point theorem, the existence results of positive solution are obtained.

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##### ISRP Style

TINGTING QIU, ZHANBING BAI, POSITIVE SOLUTIONS FOR BOUNDARY VALUE PROBLEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION, Journal of Nonlinear Sciences and Applications, 1 (2008), no. 3, 123-131

##### AMA Style

QIU TINGTING, BAI ZHANBING, POSITIVE SOLUTIONS FOR BOUNDARY VALUE PROBLEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION. J. Nonlinear Sci. Appl. (2008); 1(3):123-131

##### Chicago/Turabian Style

QIU , TINGTING, BAI, ZHANBING. " POSITIVE SOLUTIONS FOR BOUNDARY VALUE PROBLEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION." Journal of Nonlinear Sciences and Applications, 1, no. 3 (2008): 123-131

### Keywords

• Fractional differential equation
• Positive solution
• Fixed-point theorem.

•  34B15
•  34B18

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