Research Projects

This research examines nonlinear dynamics and synchronization via the lens of fractional calculus and its potential to address the tremendous complexity of contemporary systems. Fractional-order models are typically thought to possess memory and hereditary characteristics. Consequently, they inherently offer a broader range than traditional integer-order methods in the nondeterministic context of analysis and control, unlike most other contemporary approaches to such analyses and controls. The project will primarily focus on the development of mathematical models, control strategies for synchronization, and the examination of stability and robustness in systems characterized by fractional orders. Primary applications encompass secure communication, power grid stability challenges, and biophysical modeling. It aims to explore the uncharted domain of theoretical frameworks for fractional-order dynamics and synchronization, facilitating innovative applications in science and engineering - essential tools for addressing complex systems influenced by memory effects.