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Existence on positive solutions for boundary value problems of singular nonlinear fractional differential equations

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4 Author(s)
Yige Zhao ; Sch. of Sci., Univ. of Jinan, Jinan, China ; Shurong Sun ; Zhenlai Han ; Meng Zhang

In this paper, we study the existence of positive solutions for the singular nonlinear fractional differential equation boundary value problem D0+α u(t) + f(t,u(t)) = 0, 0 <; t <; 1, u(0) = u(1) = u'(0) = 0, where 2 <; α ≤ 3 is a real number, D0+α is the Riemann-Liouville fractional derivative, and f : (0,1] × [0, + ∞) → [0, + ∞) is continuous, limt→0+ f(t, ·) = + ∞ (i.e., f is singular at t = 0). Our analysis rely on nonlinear alternative of Leray-Schauder type and Krasnosel'skii fixed point theorem on a cone. As an application, an example is presented to illustrate the main results.

Published in:

Mechatronics and Embedded Systems and Applications (MESA), 2010 IEEE/ASME International Conference on

Date of Conference:

15-17 July 2010

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