Synchronization of Chaotic Satellite Systems with Fractional Derivatives Analysis Using Feedback Active Control Techniques

This research article introduces a novel chaotic satellite system based on fractional derivatives. The study explores the characteristics of various fractional derivative satellite systems through detailed phase portrait analysis and computational simulations, employing fractional calculus. We provide illustrations and tabulate the phase portraits of these satellite systems, highlighting the influence of different fractional derivative orders and parameter values. Notably, our findings reveal that chaos can occur even in systems with fewer than three dimensions. To validate our results, we utilize a range of analytical tools, including equilibrium point analysis, dissipative measures, Lyapunov exponents, and bifurcation diagrams. These methods confirm the presence of chaos and offer insights into the system's dynamic behavior. Additionally, we demonstrate effective control of chaotic dynamics using feedback active control techniques, providing practical solutions for managing chaos in satellite systems.