Geodesic
Existence of unbounded positive solutions for BVPs of singular fractional differential equations
Liu, Yuji1 ; Shi, Haiping2
1 Department of Mathematics, Guangdong University of Business Studies, Guangzhou 510320, P. R. China
2 Basic Courses Department, Guangdong Construction Vocational Technology Institute, Guangzhou 510450, P. R. China
Journal of nonlinear sciences and its applications, Tome 5 (2012) no. 4, p. 281-293.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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 $t = 1$.
DOI : 10.22436/jnsa.005.04.04
Classification : 34B37, 65L05, 92D25
Keywords: Singular fractional differential equation, boundary value problem, unbounded positive solution, Fixed Point Theorem.

Liu, Yuji 1 ; Shi, Haiping 2

1 Department of Mathematics, Guangdong University of Business Studies, Guangzhou 510320, P. R. China
2 Basic Courses Department, Guangdong Construction Vocational Technology Institute, Guangzhou 510450, P. R. China 
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Liu, Yuji; Shi, Haiping. Existence of unbounded positive solutions for BVPs of singular fractional differential equations. Journal of nonlinear sciences and its applications, Tome 5 (2012) no. 4, p. 281-293. doi : 10.22436/jnsa.005.04.04. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.005.04.04/

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