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
Author(s): J. F. Gómez-Aguilar, Abdon Atangana
Publisher: CRC Press/Chapman & Hall
Year: 2022
Language: English
Pages: 576
City: Boca Raton
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
