This book focuses on the applications of various types of fractional-order differential equations. The authors present their latest research results. This book for the first time introduces the concept of general fractional chaotic systems and their synchronisation, investigates the synchronisation of a fractional coupled reaction-diffusion system using a sliding mode control approach, and considers the impacts of fear and prey escape on a fractional-order prey-predator system with Beddington-DeAngelis functional response. Authors believe that these recent research results can promote the applications of fractional-order differential equations in diverse areas.
The book will be attractive to researchers in various fields of mathematics, biomathematics and engineering. Graduate students in related fields may also find this book useful.
Chapter 1. Introduction.- Part I. Control and Synchronization of Several Classes of General Fractional Systems.- Chapter 2. Adaptive Sliding Mode Control for Uncertain General Fractional Chaotic Systems.- Chapter 3. Synchronization of Uncertain General Fractional Unified Chaotic Systems via Finite-Time Adaptive Sliding Mode Control.- Chapter 4. Finite-time Synchronization of Delayed Fractional-order Heterogeneous Complex Networks.- Chapter 5. Mittag-Leffler Synchronization of Fractional-order Memristor-based Neural Networks with Leakage and Time-varying Delays.- Part II. Stability, Control and Synchronization of Several Classes of Fractional Reaction-Diffusion Systems.- Chapter 6. Global ML Stability of the Delayed Fractional-order Coupled Reaction-Diffusion System on Networks Without Strong Connectedness.- Chapter 7. Global Mittag-Leffler Synchronization of Coupled Delayed Fractional Reaction-Diffusion Cohen-Grossberg Neural Networks via Sliding Mode Control.- Chapter 8. Projective Synchronization for Uncertain Fractional Reaction-Diffusion Systems via Adaptive Sliding Mode Control based on Finite-Time Scheme.- Part III. Dynamic Behavior of Fractional-order System with Functional Response Function.- Chapter 9. Impact of Fear Effect and Prey Refuge on a Fractional Order Prey-Predator System with Beddington-DeAngelis Functional Response.- Chapter 10. A Fractional-order Food Chain System Incorporating Holling-II type Functional Response and Prey Refuge.
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