Electron. J. Diff. Equ., Vol. 2012 (2012), No. 80, pp. 1-10.

Positive solutions for fractional differential equations with variable coefficients

Yi Chen, Zhanmei Lv

Abstract:
In this article, we study the existence of the positive solutions for a class of differential equations of fractional order with variable coefficients. The equation of this type plays an important role in the description and modeling of control systems, such as $PD^{\mu}$-controller. The differential operator is taken in the Riemann-Liouville sense. Our analysis relies on the Leggett-Williams fixed point theorem.

Submitted April 3, 2012. Published May 18, 2012.
Math Subject Classifications: 26A33, 34A08, 34A12.
Key Words: Fractional differential equations; fixed point theorem; positive solution; multiplicity solution.

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Yi Chen
School of Mathematical Sciences and Computing Technology
Central South University
Changsha, Hunan 410083, China
email: mathcyt@163.com
Zhanmei Lv
School of Mathematical Sciences and Computing Technology
Central South University
Changsha, Hunan 410083, China
email: cy2008csu@163.com

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