Hindawi Publishing Corporation Advances in Difference Equations Volume 2011, Article ID 213485, 17 pages doi: Research Article Stability Analysis of Fractional Differential Systems with Order Lying in 1, 2 Fengrong Zhang1, 2 and Changpin Li1 1 2 Department of Mathematics, Shanghai University, Shanghai 200444, China School of Mathematics and Computational Science, China University of Petroleum (East China), Dongying 257061, China Correspondence should be addressed to Changpin Li, lcp@ Received 6 December 2010; Revised 31 December 2010; Accepted 7 March 2011 Academic Editor: Dumitru Baleanu Copyright q 2011 F. Zhang and C. Li. This is an open access article distributed under the Creative Commons Attribution License,. | Hindawi Publishing Corporation Advances in Difference Equations Volume 2011 Article ID 213485 17 pages doi 2011 213485 Research Article Stability Analysis of Fractional Differential Systems with Order Lying in 1 2 Fengrong Zhang1 2 and Changpin Li1 1 Department of Mathematics Shanghai University Shanghai 200444 China 2 School of Mathematics and Computational Science China University of Petroleum East China Dongying 257061 China Correspondence should be addressed to Changpin Li lcp@ Received 6 December 2010 Revised 31 December 2010 Accepted 7 March 2011 Academic Editor Dumitru Baleanu Copyright 2011 F. Zhang and C. Li. 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. The stability of n-dimensional linear fractional differential systems with commensurate order 1 a 2 and the corresponding perturbed systems is investigated. By using the Laplace transform the asymptotic expansion of the Mittag-Leffler function and the Gronwall inequality some conditions on stability and asymptotic stability are given. 1. Introduction Fractional calculus has a long history with more than three hundred years 1-3 . Up to now it has been proved that fractional calculus is very useful. Many mathematical models of real problems arising in various fields of science and engineering were established with the help of fractional calculus such as viscoelastic systems dielectric polarization electrodeelectrolyte polarization and electromagnetic waves 4-7 . Recently the stability theory of fractional differential equations FDEs is of main interest in physical systems. Moreover some stability results have been found 8-17 . These stability results are almost about the linear fractional differential systems with commensurate order . the fractional derivative order has to be an integer multiple of minimal fractional order 18
