This book is about the simulation and modeling of novel chaotic systems within the frame of fractal-fractional operators. The methods used, their convergence, stability, and error analysis are given, and this is the first book to offer mathematical modeling and simulations of chaotic problems with a wide range of fractal-fractional operators, to find solutions.
Numerical Methods for Fractal-Fractional Differential Equations and Engineering: Simulations and Modeling provides details for stability, convergence, and analysis along with numerical methods and their solution procedures for fractal-fractional operators. The book offers applications to chaotic problems and simulations using multiple fractal-fractional operators and concentrates on models that display chaos. The book details how these systems can be predictable for a while and then can appear to become random.
Practitioners, engineers, researchers, and senior undergraduate and graduate students from mathematics and engineering disciplines will find this book of interest._
1. Basic principle of nonlocalities. 2. Basic of fractional operators. 3. Definitions of fractal-fractional operators with numerical approximations. 4. Error analysis. 5. Existence and uniqueness of fractal fractional differential equations. 6. A numerical solution of fractal-fractional ODE with linear interpolation. 7. Numerical scheme of fractal-fractional ODE with middle point interpolation. 8. Fractal-Fractional Euler method. 9. Application of fractal-fractional operators to a chaotic model. 10. Fractal-fractional Modified Chua chaotic attractor. 11. Application of fractal-fractional operators to study a new chaotic model. 12. Fractal-fractional operators and their application to a chaotic system with sinusoidal component. 13. Application of fractal-fractional operators to four-scroll chaotic system. 14. Application of fractal-fractional operators to a novel chaotic model. 15. A 4D chaotic system under fractal-fractional operators. 16. Self-excited and hidden attractors through fractal-fractional operators. 17. Dynamical analysis of a chaotic model in fractal-fractional operators. 18. A chaotic cancer model in fractal-fractional operators. 19. A multiple chaotic attractor model under fractal-fractional operators. 20. The dynamics of multiple chaotic attractor with fractal-fractional operators. 21. Dynamics of 3D chaotic systems with fractal-fractional operators. 22. The hidden attractors model with fractal-fractional operators. 23. An SIR epidemic model with Fractal-fractional derivative. 24. Application of fractal-fractional operators to COVID-19 infection.