Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 09, pp. 1-11.

Title: Existence of solutions to fractional order ordinary and delay
       differential equations and applications

Author: Syed Abbas (Indian Institute of Technology, Mandi, India)

Abstract:
 In this article, we discuss the existence and uniqueness of
 solution to fractional order ordinary and delay differential
 equations. We apply our results on the single species model of
 Lotka Volterra type. Fixed point theorems are the main tool used
 here to establish the existence and uniqueness results. First we
 use Banach contraction principle and then Krasnoselskii's fixed
 point theorem to show the existence and uniqueness of the solution
 under certain conditions. Moreover, we prove that the solution can
 be extended to maximal interval of existence.

Submitted November 16, 2010. Published January 16, 2011.
Math Subject Classifications: 34K40, 34K14.
Key Words: Fractional differential equation;
 fixed point theorems; maximum interval of existence.