POSITIVE SOLUTIONS FOR BOUNDARY VALUE PROBLEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION
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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.
Share and Cite
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.
MSC
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