Advances in Dynamics and Control of Fractional Discrete Time Systems

Adel Ouannas received his B.S. in Mathematics from Laarbi Ben Mhidi University in 2003, an M.Sc. from the University of Constatine in 2006, and a Ph.D. from the same university in 2015. He is a Full Professor of Applied and Computational Mathematics at Larbi Ben M’hidi University of Oum El Bouaghi, Algeria. He has authored and co-authored more than 370 scientific publications in internationally recognized peer-reviewed journals, with research interests encompassing fractional calculus, nonlinear dynamical systems, chaos theory, and mathematical modeling. He is currently serving as a Visiting Professor at the Islamic University of Madinah, Saudi Arabia.Noureddine Djenina is a Lecturer in Mathematics at the University of El-Chahid Mustapha Ben Boulaid Batna 2, Algeria. He holds a PhD in Applied Mathematics from Larbi Ben M'hidi University of Oum El Bouaghi, Algeria, and a Master's degree in Partial Differential Equations and Applications from Cheikh Larbi Tebessi University, Algeria. His research interests include fractional calculus, stability theory, synchronization, and epidemic modeling. Omar Naifar earned his Master’s degree in Computer Science in 2010, a Ph.D. in Electrical Engineering in 2015, and the H.D.R. degree in 2021, all from the University of Sfax, Tunisia. He is currently an Associate Professor and a member of the Control and Energy Management Laboratory (CEM-Lab). His research interests include robust nonlinear control, observer design, fault diagnosis, and fractional-order systems. Prof. Naifar is an Associate Editor of the Asian Journal of Control (Wiley). Abdellatif Ben Makhlouf received his Bachelor’s and Master’s degrees in Mathematics and his Ph.D. from the University of Sfax, Tunisia, in 2015. He is an Associate Professor of Mathematics at University of Sfax, Tunisia. His current research interests include Fractional Differential Equations, Ordinary Differential Equations, Stochastic Differential Equations, Control Theory and Stability Theory.

• 1. Introduction. Definition and importance of fractional difference systems2. Essential Mathematical Tools. Z-transform, state matrices, and stability theory3. Fundamentals of Fractional Difference Calculus. Basic concepts and properties4. Modeling of Fractional Discrete-Time Systems. Methods for building mathematical models5. Stability of Commensurate Order Systems. Stability criteria and analysis6. Stability of Incommensurate Order Systems. Advanced methods and analyses7. Control Methods in Fractional Discrete-Time Systems. Various control techniques8. Synchronization in Fractional Discrete-Time Systems. Study and mechanisms of synchronization9. Control of Chaos in Fractional Discrete-Time Systems. Exploring the Control in chaotic Fractional Discrete-Time Systems10. Applications of Fractional Discrete-Time Systems in Engineering and Science. Practical examples and uses11. Applications in Epidemic Models. Studying the role of fractional discrete systems in modeling the spread of infectious diseases, stability of disease-free equilibrium, and control strategies12. Numerical Algorithms. Computational methods for solving fractional equations13. Design of Robust Control Systems. Strategies for performance improvement14. Conclusion and Future Perspectives. Summary and future research suggestions