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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
Table of Contents
Chapter 1: Chaos and Multiple Attractors in Fractional Financial Model
Rahat Zarin, Ebenezer Bonyah, Md. Nur Alam
Chapter 2: Time-Fractional Optimal Control for Constrained Systems Involving Mittag-Leffler Non-Singular Kernel
G.M. Bahaa, A. Hamiaz, W. Abuelela
Chapter 3: Signal Reconstruction by using State Observers for Fractional-Order Chaotic Systems with Application to Secure Communications
Juan J. Montesinos-García, Rafael Martínez-Guerra
Chapter 4: On Fractal Structure and co-existing Hidden Attractors in Models with Mittag-Leffler Kernel
Emile Franc Doungmo Goufo
Chapter 5: Compound Structure with a Fractal Type Representation for Fractional Models
Emile Franc Doungmo Goufoa, Abdon Atangana
Chapter 6: A Behavior of Shallow Water Wave under Mittag-Leffler Law
Emile Franc Doungmo Goufoa, PM Tchepmo Djomegni, M Mbehou, SB Mugisha
Chapter 7: On Solutions of Fractional Klein–Gordon Equations
Ali Akgül
Chapter 8: Reproducing Kernel Method for Solutions of Fractal Fractional Differential Equations
Ali Akgül
Chapter 9: Stability of Fractional Nonlinear Systems with Mittag-Leffler Kernel and Design of State Observers
Oscar Martínez-Fuentes, Sergio M. Delfín-Prieto
Chapter 10: Coexistence of Chaotic Attractors in a Four-Dimensional Memristor-based Chaotic Non-Local System: Analysis and FPGA Implementation
E. Zambrano-Serrano, C. Posadas-Castillo, M.A. Platas-Garza
Chapter 11: New Chaotic Attractor Captured with Fractal-Fractional Differential and Integral Operators
Abdon Atangana, Sonal Jain
Chapter 12: New Results in Modeling Herd Behavior in Ecological Interaction
Salih Djilali, Soufiane Bentout, Behzad Ghanbari
Chapter 13: Double Integration for the Fractional Advection-Dispersion Equation with Non-Singular Derivative
Ndolane Sene
Chapter 14: Numerical Methods for Solving Systems of Atangana-Baleanu Fractional Differential Equations
Dumitru Baleanu, Babak Shiri
Chapter 15: Use of Real Data Application for Analysis of the Measles Disease under Caputo-Fabrizio-Caputo Operator
Sania Qureshi, Zaib-un-Nisa Memon
Chapter 16: Crank-Nicolson Quasi Wavelet Method for the Numerical Solution of Variable Order Time Space RIESZ Fractional Reaction-Diffusion Equation
Sachin Kumar
Chapter 17: Fractional Optimal Control Model for Nutrient-Phytoplankton-Zooplankton
Ebenezer Bonyah
Chapter 18: Comparative Numerical Results Considering Fractional Derivative and Memory Dependent Derivative in Modeling RL and RC Electrical Circuits
Norodin A. Rangaig, Alvanh Alem G. Pido, Dumitru Baleanu
Chapter 19: Solution of Fractional Langevin Equation with Exponential Kernel and its Anomalous Relaxation Function
Norodin A. Rangaig, Alvanh Alem G. Pido, Caironesa P. Dulpina
Chapter 20: A Mathematical Model on Prostitution And Drug (Alcohol) Misuse: The Menacing Combination with Exponential Law Optimal Control
E. Bonyaha, Amma Achiaa
Chapter 21: Another Aspect of Fractional Langevin Motion Driven by Fractional Gaussian Noise involving Caputo-Fabrizio derivative
Norodin A. Rangaig , Alvanh Alem G. Pido, Caironesa P. Dulpina
