Applications of Fractional Calculus to Modeling in Dynamics and Chaos

Description

Applications of Fractional Calculus to Modeling in Dynamics and Chaos aims to present novel developments, trends, and applications of fractional-order derivatives with power law and Mittag-Leffler kernel in the areas of chemistry, mechanics, chaos, epidemiology, fluid mechanics, modeling, and engineering. Non-singular and non-local fractional-order derivatives have been applied in different chapters to describe complex problems. The book offers theory and practical applications for the solutions of real-life problems and will be of interest to graduate-level students, educators, researchers, and scientists interested in mathematical modeling and its diverse applications. Features Discusses real-world problems, theory, and applications Covers new developments and advances in the various areas of nonlinear dynamics, signal processing, and chaos Suitable to teach master’s and/or PhD-level graduate students, and can be used by researchers, from any field of the social, health, and physical sciences Cover Half Title Title Page Copyright Page Contents About the Editors List of Contributors CHAPTER 1: Chaos and Multiple Attractors in the Fractional Financial Model CHAPTER 2: Time-Fractional Optimal Control for Constrained Systems Involving Mittag-Leffler Nonsingular Kernel CHAPTER 3: Signal Reconstruction by Using State Observers for Fractional-Order Chaotic Systems with Application to Secure Communications CHAPTER 4: On Fractal Structure and Coexisting Hidden Attractors in Models with Mittag-Leffler Kernel CHAPTER 5: Compound Structure with a Fractal Type Representation for Fractional Models CHAPTER 6: A Behavior of Shallow-Water Wave under Mittag-Leffler Law CHAPTER 7: On Solutions of Fractional Klein-Gordon Equations CHAPTER 8: Reproducing Kernel Method for Solutions of Fractal-Fractional Differential Equations CHAPTER 9: Observer Design for Nonlinear Fractional-Order Systems with Mittag-Leffler Kernel CHAPTER 10: Coexistence of Chaotic Attractors in a Four-Dimensional Memristor-Based Chaotic Nonlocal System: Analysis and FPGA Implementation CHAPTER 11: New Chaotic Attractor Captured with Fractal-Fractional Differential and Integral Operators CHAPTER 12: New Results in Modeling Herd Behavior in Ecological Interaction CHAPTER 13: Double Integration for the Fractional Advection-Dispersion Equation with Nonsingular Derivative CHAPTER 14: Numerical Methods for Solving Systems of Atangana-Baleanu Fractional Differential Equations CHAPTER 15: Use of Real Data Application for Analysis of the Measles Disease under Caputo-Fabrizio-Caputo Operator CHAPTER 16: Crank-Nicolson Quasi-Wavelet Method for the Numerical Solution of Variable-Order Time-Space Riesz Fractional Reaction-Diffusion Equation CHAPTER 17: Fractional Optimal Control Model for Nutrients, Phytoplankton, and Zooplankton CHAPTER 18: Comparative Numerical Results Considering Fractional Derivative and Memory Dependent Derivative in Modeling RL and RC Electrical Circuits CHAPTER 19: Solution of Fractional Langevin Equation with Exponential Kernel and Its Anomalous Relaxation Function CHAPTER 20: A Mathematical Model on Prostitution and Drug (Alcohol) Misuse: The Menacing Combination with Exponential Law Optimal Control CHAPTER 21: Another Aspect of Fractional Langevin Motion Driven by Fractional Gaussian Noise Involving Caputo-Fabrizio Derivative Index