Hindawi Publishing Corporation International Journal of Differential Equations Volume 2011, Article ID 250763, 13 pages doi:10.1155/2011/250763 Research Article Antisynchronization of Nonidentical Fractional-Order Chaotic Systems Using Active Control Sachin Bhalekar 1 and Varsha Daftardar-Gejji 2 1 Department of Mathematics, Shivaji University, Vidyanagar, Kolhapur 416004, India 2 Department of Mathematics, University of Pune, Ganeshkhind, Pune 411007, India Correspondence should be addressed to Varsha Daftardar-Gejji, vsgejji@gmail.com Received 7 May 2011; Accepted 16 July 2011 Academic Editor: Wen Chen Copyright q 2011 S. Bhalekar and V. Daftardar-Gejji. 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. Antisynchronization phenomena are studied in nonidentical fractional-order differential systems. The characteristic feature of antisynchronization is that the sum of relevant state-variables vanishes for sufficiently large value of time variable. Active control method is used first time in the literature to achieve antisynchronization between fractional-order Lorenz and Financial systems, Financial and Chen systems, and L ¨ u and Financial systems. The stability analysis is carried out using classical results. We also provide numerical results to verify the effectiveness of the proposed theory. 1. Introduction In their pioneering work 1, 2, Pecora and Carroll have shown that chaotic systems can be synchronized by introducing appropriate coupling. The notion of synchronization of chaos has further been explored in secure communications of analog and digital signals 3 and for developing safe and reliable cryptographic systems 4. For the synchronization of chaotic systems, a variety of approaches have been proposed which include nonlinear feedback 5, adaptive 6, 7, and active controls 8, 9. Antisynchronization AS is a phenomenon in which the state vectors of the synchro- nized systems have the same amplitude but opposite signs to those of the driving system. Hence the sum of two signals converges to zero when AS appears. Antisynchronization has applications in lasers 10, in periodic oscillators, and in communication systems. Using AS to lasers, one may generate not only drop-outs of the intensity but also short pulses of high intensity, which results in the pulses of special shapes.