Existence of unbounded positive solutions for BVPs of singular fractional differential equations
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Authors
Yuji Liu
- Department of Mathematics, Guangdong University of Business Studies, Guangzhou 510320, P. R. China.
Haiping Shi
- Basic Courses Department, Guangdong Construction Vocational Technology Institute, Guangzhou 510450, P. R. China.
Abstract
In this article, we establish the existence of multiple unbounded positive solutions to the boundary value
problem of the nonlinear singular fractional differential equation
\[
\begin{cases}
D^\alpha_{ 0^+}u(t) + f(t; u(t)) = 0; t \in (0; 1); 1 < \alpha < 2,\\
[I^{2-\alpha}_{ 0^+} u(t)]'|_{t=0} = 0\\
u(1) = 0.
\end{cases}
\]
Our analysis relies on the well known fixed point theorems in the cones in Banach spaces. Here \(f\) is singular
at \(t = 0\) and \(t = 1\).
Share and Cite
ISRP Style
Yuji Liu, Haiping Shi, Existence of unbounded positive solutions for BVPs of singular fractional differential equations, Journal of Nonlinear Sciences and Applications, 5 (2012), no. 4, 281--293
AMA Style
Liu Yuji, Shi Haiping, Existence of unbounded positive solutions for BVPs of singular fractional differential equations. J. Nonlinear Sci. Appl. (2012); 5(4):281--293
Chicago/Turabian Style
Liu, Yuji, Shi, Haiping. "Existence of unbounded positive solutions for BVPs of singular fractional differential equations." Journal of Nonlinear Sciences and Applications, 5, no. 4 (2012): 281--293
Keywords
- Singular fractional differential equation
- boundary value problem
- unbounded positive solution
- Fixed Point Theorem.
MSC
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