Applications of Fractional Calculus to Modeling in Dynamics and Chaos

ISBN-13: 9780367438876 / Angielski / Twarda / 2022 / 512 str.

J. F. Gómez-Aguilar; Abdon Atangana

Opis

This book 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.

Spis treści

1. Chaos and Multiple Attractors in Fractional Financial Model. 2. Time-Fractional Optimal Control for Constrained Systems Involving Mittag-Leffler Non-Singular Kernel. 3. Signal Reconstruction by using State Observers for Fractional-Order Chaotic Systems with Application to Secure Communications. 4. On Fractal Structure and co-existing Hidden Attractors in Models with Mittag-Leffler Kernel. 5. Compound Structure with a Fractal Type Representation for Fractional Models. 6. A Behavior of Shallow Water Wave under Mittag-Leffler Law. 7. On Solutions of Fractional Klein–Gordon Equations. 8. Reproducing Kernel Method for Solutions of Fractal Fractional Differential Equations. 9. Stability of Fractional Nonlinear Systems with Mittag-Leffler Kernel and Design of State Observers. 10. Coexistence of Chaotic Attractors in a Four-Dimensional Memristor-based Chaotic Non-Local System. Analysis and FPGA Implementation. 11. New Chaotic Attractor Captured with Fractal-Fractional Differential and Integral Operators. 12. New Results in Modeling Herd Behavior in Ecological Interaction. 13. Double Integration for the Fractional Advection-Dispersion Equation with Non-Singular Derivative. 14. Numerical Methods for Solving Systems of Atangana-Baleanu Fractional Differential Equations. 15. Use of Real Data Application for Analysis of the Measles Disease under Caputo-Fabrizio-Caputo Operator. 16. Crank-Nicolson Quasi Wavelet Method for the Numerical Solution of Variable Order Time Space RIESZ Fractional Reaction-Diffusion Equation. 17. Fractional Optimal Control Model for Nutrient-Phytoplankton-Zooplankton. 18. Comparative Numerical Results Considering Fractional Derivative and Memory Dependent Derivative in Modeling RL and RC Electrical Circuits. 19. Solution of Fractional Langevin Equation with Exponential Kernel and its Anomalous Relaxation Function. 20. A Mathematical Model on Prostitution and Drug (Alcohol) Misuse. The Menacing Combination with Exponential Law Optimal Control. 21. Another Aspect of Fractional Langevin Motion Driven by Fractional Gaussian Noise involving Caputo-Fabrizio derivative