Positive solutions for Caputo fractional differential equations involving integral boundary conditions
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Authors
Yong Wang
- School of Science, Jiangnan University, Wuxi 214122, China.
Yang Yang
- School of Science, Jiangnan University, Wuxi 214122, China.
Abstract
In this work we study integral boundary value problem involving Caputo differentiation
\[
\begin{cases}
^c D^q_t u(t)= f(t,u(t)),\,\, 0<t<1,\\
\alpha u(0)-\beta u(1)=\int^1_0 h(t)u(t)dt, \gamma u'(0)-\delta u'(1)\int^1_0 g(t)u(t)dt,
\end{cases}
\]
where \(\alpha,\beta,\gamma,\delta\)
are constants with \(\alpha>\beta>0,\gamma>\delta>0, f\in C([0,1]\times \mathbb{R}^+,\mathbb{R}), g,h\in C([0,1],\mathbb{R}^+)\) and \( ^c D^q_t\)
is the standard Caputo fractional derivative of fractional order \(q(1 < q < 2)\). By using some fixed point
theorems we prove the existence of positive solutions.
Share and Cite
ISRP Style
Yong Wang, Yang Yang, Positive solutions for Caputo fractional differential equations involving integral boundary conditions, Journal of Nonlinear Sciences and Applications, 8 (2015), no. 2, 99--109
AMA Style
Wang Yong, Yang Yang, Positive solutions for Caputo fractional differential equations involving integral boundary conditions. J. Nonlinear Sci. Appl. (2015); 8(2):99--109
Chicago/Turabian Style
Wang, Yong, Yang, Yang. "Positive solutions for Caputo fractional differential equations involving integral boundary conditions." Journal of Nonlinear Sciences and Applications, 8, no. 2 (2015): 99--109
Keywords
- Caputo fractional boundary value problem
- fixed point theorem
- positive solution.
MSC
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