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Abstract and Applied Analysis
Volume 2010 (2010), Article ID 762857, 16 pages
http://dx.doi.org/10.1155/2010/762857
Research Article

Fractional Differential Equations in Terms of Comparison Results and Lyapunov Stability with Initial Time Difference

Department of Mathematics, Gebze Institute of Technology, Gebze-Kocaeli 141-41400, Turkey

Received 16 September 2009; Revised 29 November 2009; Accepted 7 January 2010

Academic Editor: Dumitru Bǎleanu

Copyright © 2010 Coşkun Yakar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The qualitative behavior of a perturbed fractional-order differential equation with Caputo's derivative that differs in initial position and initial time with respect to the unperturbed fractional-order differential equation with Caputo's derivative has been investigated. We compare the classical notion of stability to the notion of initial time difference stability for fractional-order differential equations in Caputo's sense. We present a comparison result which again gives the null solution a central role in the comparison fractional-order differential equation when establishing initial time difference stability of the perturbed fractional-order differential equation with respect to the unperturbed fractional-order differential equation.