Electron. J. Diff. Equ., Vol. 2012 (2012), No. 70, pp. 1-8.

Uniqueness of positive solutions for a fractional differential equation via a fixed point theorem of a sum operator

Chen Yang, Chengbo Zhai

In this work, we study the existence and uniqueness of positive solutions for nonlinear fractional differential equation boundary-value problems. Our analysis relies on a fixed point theorem of a sum operator. Our results guarantee the existence of a unique positive solution, and can be applied for constructing an iterative scheme for obtaining the solution.

Submitted January 27, 2012. Published May 7, 2012.
Math Subject Classifications: 34B18.
Key Words: Riemann-Liouville fractional derivative; positive solution; fractional differential equation; existence and uniqueness; fixed point theorem.

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Chen Yang
Department of Mathematics
Business College of Shanxi University
Taiyuan 030031 Shanxi, China
email: yangchen0809@126.com
Chengbo Zhai
School of Mathematical Sciences, Shanxi University
Taiyuan 030006 Shanxi, China
email: cbzhai@sxu.edu.cn, cbzhai215@sohu.com

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