# Existence of unbounded positive solutions for BVPs of singular fractional differential equations

Volume 5, Issue 4, pp 281--293
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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.

•  34B37
•  65L05
•  92D25

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