Abstract and Applied Analysis
Volume 2010 (2010), Article ID 108651, 7 pages
doi:10.1155/2010/108651
Research Article

Mittag-Leffler Stability Theorem for Fractional Nonlinear Systems with Delay

S. J. Sadati,1 D. Baleanu,2,3 A. Ranjbar,1 R. Ghaderi,1 and T. Abdeljawad (Maraaba)3

1Department of Electrical and Computer Engineering, Faculty of Electrical Engineering, Babol Noshirvani University of Technology, Babol, Iran
2Department of Mathematics and Computer Science, Faculty of Arts and Sciences, Çankaya University, 06530 Ankara, Turkey
3Institute of Space Sciences, P.O. Box MG-23, 76900 Magurele-Bucharest, Romania

Received 3 May 2010; Accepted 14 July 2010

Academic Editor: Allan C. Peterson

Copyright © 2010 S. J. Sadati et al. 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

Fractional calculus started to play an important role for analysis of the evolution of the nonlinear dynamical systems which are important in various branches of science and engineering. In this line of taught in this paper we studied the stability of fractional order nonlinear time-delay systems for Caputo's derivative, and we proved two theorems for Mittag-Leffler stability of the fractional nonlinear time delay systems.