Advances in Dynamics and Control of Fractional Discrete Time Systems: Theories and Applications delves into the cutting-edge developments in the field of fractional discrete time systems. This comprehensive resource bridges the gap between theoretical advancements and practical applications, offering readers a thorough understanding of the dynamics and control mechanisms of these systems. With a blend of rigorous mathematical theory and real-world examples, this book is an essential guide for anyone looking to master the complexities of fractional discrete time systems.
1. Chapter 1: General introduction and overview of the book - p. 1 2. Chapter 2: Fractional discrete calculus: theory, methods, and approaches - p. 13 3. Chapter 3: Stability of commensurate fractional discrete time systems - p. 43 4. Chapter 4: Stability and simulation of incommensurate fractional discrete systems - p. 75 5. Chapter 5: Stability of fractional discrete systems with nabla-operator - p. 101 6. Chapter 6: Stability analysis in fractional h-difference systems: linear and nonlinear approaches - p. 123 7. Chapter 7: Lyapunov functions for Caputo fractional difference systems with incommensurate orders - p. 145 8. Chapter 8: Stability analysis of fractional variable-order discrete-time systems - p. 163 9. Chapter 9: Application of discrete fractional calculus in analyzing the COVID-19 epidemic - p. 187 10. Chapter 10: Modeling Ebola transmission using a discrete fractional incommensurate approach - p. 211 11. Chapter 11: Chaos analysis and stabilization in the fractional variable-order Grassi–Miller map - p. 235 12. Chapter 12: Four-dimensional fractional-order chaotic map: dynamical properties with constant and variable orders - p. 273 13. Chapter 13: Impact of fractional variable order on the discrete-time Tinkerbell map dynamics - p. 305 14. Chapter 14: On chaotic behavior of a fractional discrete-time model for computer virus spread - p. 331 15. Chapter 15: Control of fractional discrete chaotic systems - p. 357 16. Chapter 16: Linear techniques for chaos control in fractional-order discrete systems - p. 385 17. Chapter 17: On different synchronization strategies of fractional chaotic discrete-time systems - p. 417 18. Chapter 18: Nonlocal pattern formation: a nabla fractional framework for discrete Gierer–Meinhardt dynamics - p. 451 19. Chapter 19: Finite-time stability criteria for a discrete fractional-order SIR reaction–diffusion epidemic model - p. 477 20. Index - p. 503
Advances in Dynamics and Control of Fractional Discrete Time Systems: Theories and Applications delves into the cutting-edge developments in the field of fractional discrete time systems. This comprehensive resource bridges the gap between theoretical advancements and practical applications, offering readers a thorough understanding of the dynamics and control mechanisms of these systems. With a blend of rigorous mathematical theory and real-world examples, this book is an essential guide for anyone looking to master the complexities of fractional discrete time systems.
1. Chapter 1: General introduction and overview of the book - p. 1 2. Chapter 2: Fractional discrete calculus: theory, methods, and approaches - p. 13 3. Chapter 3: Stability of commensurate fractional discrete time systems - p. 43 4. Chapter 4: Stability and simulation of incommensurate fractional discrete systems - p. 75 5. Chapter 5: Stability of fractional discrete systems with nabla-operator - p. 101 6. Chapter 6: Stability analysis in fractional h-difference systems: linear and nonlinear approaches - p. 123 7. Chapter 7: Lyapunov functions for Caputo fractional difference systems with incommensurate orders - p. 145 8. Chapter 8: Stability analysis of fractional variable-order discrete-time systems - p. 163 9. Chapter 9: Application of discrete fractional calculus in analyzing the COVID-19 epidemic - p. 187 10. Chapter 10: Modeling Ebola transmission using a discrete fractional incommensurate approach - p. 211 11. Chapter 11: Chaos analysis and stabilization in the fractional variable-order Grassi–Miller map - p. 235 12. Chapter 12: Four-dimensional fractional-order chaotic map: dynamical properties with constant and variable orders - p. 273 13. Chapter 13: Impact of fractional variable order on the discrete-time Tinkerbell map dynamics - p. 305 14. Chapter 14: On chaotic behavior of a fractional discrete-time model for computer virus spread - p. 331 15. Chapter 15: Control of fractional discrete chaotic systems - p. 357 16. Chapter 16: Linear techniques for chaos control in fractional-order discrete systems - p. 385 17. Chapter 17: On different synchronization strategies of fractional chaotic discrete-time systems - p. 417 18. Chapter 18: Nonlocal pattern formation: a nabla fractional framework for discrete Gierer–Meinhardt dynamics - p. 451 19. Chapter 19: Finite-time stability criteria for a discrete fractional-order SIR reaction–diffusion epidemic model - p. 477 20. Index - p. 503
