Applications of Fractional Calculus to Modeling in Dynamics and Chaos

J. F. Gómez-Aguilar, Abdon Atangana, J. F. Gómez-Aguilar, Abdon Atangana

• Publisher: Chapman and Hall/CRC
• Year: 2022
• Print ISBN: 9780367438876
• eBook ISBN: 9781000597615
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

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

Table of contents

• Cover Page
• Half-Title Page
• 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