Numerical methods for fractal-fractional differential equations and engineering : simulations and modeling
著者
書誌事項
Numerical methods for fractal-fractional differential equations and engineering : simulations and modeling
（Mathematics and its applications: modelling, engineering, and social sciences）
CRC Press, 2023
大学図書館所蔵 全1件
注記
Includes bibliographical references and index
内容説明・目次
内容説明
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._
目次
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.
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