Stability analysis, chaos control of fractional order Vallis and El-Nino systems and their synchronization

In this article the authors have studied the stability analysis and chaos control of the fractional order Vallis and El-Nino systems. The chaos control of these systems is studied using nonlinear control method with the help of a new lemma for Caputo derivative and Lyapunov stability theory. The synchronization between the systems for different fractional order cases and numerical simulation through graphical plots for different particular cases clearly exhibit that the method is easy to implement and reliable for synchronization of fractional order chaotic systems. The comparison of time of synchronization when the systems pair approaches from standard order to fractional order is the key feature of the article.