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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
About the Editors
List of Contributors
Chaos and Multiple Attractors in the Fractional Financial Model
Time-Fractional Optimal Control for Constrained Systems Involving Mittag-Leffler Nonsingular Kernel
Signal Reconstruction by Using State Observers for Fractional-Order Chaotic Systems with Application to Secure Communications
On Fractal Structure and Coexisting Hidden Attractors in Models with Mittag-Leffler Kernel
Compound Structure with a Fractal Type Representation for Fractional Models
A Behavior of Shallow-Water Wave under Mittag-Leffler Law
On Solutions of Fractional Klein-Gordon Equations
Reproducing Kernel Method for Solutions of Fractal-Fractional Differential Equations
Observer Design for Nonlinear Fractional-Order Systems with Mittag-Leffler Kernel
Coexistence of Chaotic Attractors in a Four-Dimensional Memristor-Based Chaotic Nonlocal System: Analysis and FPGA Implementation
New Chaotic Attractor Captured with Fractal-Fractional Differential and Integral Operators
New Results in Modeling Herd Behavior in Ecological Interaction
Double Integration for the Fractional Advection-Dispersion Equation with Nonsingular Derivative
Numerical Methods for Solving Systems of Atangana-Baleanu Fractional Differential Equations
Use of Real Data Application for Analysis of the Measles Disease under Caputo-Fabrizio-Caputo Operator
Crank-Nicolson Quasi-Wavelet Method for the Numerical Solution of Variable-Order Time-Space Riesz Fractional Reaction-Diffusion Equation
Fractional Optimal Control Model for Nutrients, Phytoplankton, and Zooplankton
Comparative Numerical Results Considering Fractional Derivative and Memory Dependent Derivative in Modeling RL and RC Electrical Circuits
Solution of Fractional Langevin Equation with Exponential Kernel and Its Anomalous Relaxation Function
A Mathematical Model on Prostitution and Drug (Alcohol) Misuse: The Menacing Combination with Exponential Law Optimal Control
Another Aspect of Fractional Langevin Motion Driven by Fractional Gaussian Noise Involving Caputo-Fabrizio Derivative
Index