Fractional Calculus
Bridging Theory with Computational and Contemporary Advances
- 1st Edition - June 21, 2024
- Author: Behzad Ghanbari
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 3 - 3 1 5 0 0 - 8
- eBook ISBN:9 7 8 - 0 - 4 4 3 - 3 1 5 0 1 - 5
Fractional Calculus: Bridging Theory with Computational and Contemporary Advances is an authoritative and comprehensive guide that delves into the world of fractional calcul… Read more
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Request a sales quoteFractional Calculus: Bridging Theory with Computational and Contemporary Advances is an authoritative and comprehensive guide that delves into the world of fractional calculus, offering a unique blend of theoretical foundations, numerical algorithms, practical applications, and innovative perspectives. This book explores the mathematical framework of fractional calculus and its relevance across various disciplines, providing readers with a deep understanding of this rapidly growing field. The author presents a rigorous yet accessible approach to fractional calculus, making it suitable for mathematicians, researchers, academics, graduate students, and professionals in engineering and applied sciences. The book covers a wide range of topics, including numerical methods for fractional calculus equations, fractional differential equations, fractal dynamics, and fractional control systems. It also explores applications in areas such as physics, engineering, signal processing, and data analysis. Fractional Calculus: Bridging Theory with Computational and Contemporary Advances equips readers with the necessary tools to tackle challenging problems involving fractional calculus, empowering them to apply these techniques in their research, professional work, or academic pursuits. The book provides a comprehensive introduction to the fundamentals of fractional calculus, explaining the theoretical concepts and key definitions in a clear and accessible manner. This helps readers build a strong foundation in the subject. The book then covers a range of numerical algorithms specifically designed for fractional calculus problems, explaining the underlying principles, step-by-step implementation, and computational aspects of these algorithms. This enables readers to apply numerical techniques to solve fractional calculus problems effectively. The book also provides examples that illustrate how fractional calculus is applied to solve real-world problems, providing readers with insights into the wide-ranging applications of the subject.
- Provides a comprehensive introduction to the fundamentals of fractional calculus, explaining the theoretical concepts and key definitions in a clear and accessible manner
- Covers a range of numerical algorithms specifically designed for fractional calculus problems
- Includes practical examples and case studies from various fields such as physics, biology, finance, and signal processing
Researchers in computational modelling, applied mathematicians, and computer scientists working with researchers, engineers, and scientists in a wide range of modelling applications for engineering and scientific research. The primary audience also includes researchers and professionals in the fields of mathematics, IT, physics, engineering, biomedicine, AI, ML, biology, and healthcare
- Cover image
- Title page
- Table of Contents
- Copyright
- Dedication
- List of figures
- Biography
- Preface
- 1: Introduction to fractional calculus
- Abstract
- 1.1. What is fractional calculus?
- 1.2. Some prerequisite special functions
- 1.3. Riemann–Liouville fractional differentiation
- 1.4. Caputo fractional derivative
- 1.5. Grünwald–Letnikov derivative
- 1.6. Caputo–Fabrizio fractional differentiation
- 1.7. The Atangana–Baleanu fractional derivative and integral
- 1.8. Riesz fractional derivatives
- 1.9. The Atangana–Gómez fractional derivative
- 1.10. General fractional derivatives
- 1.11. Fractal-fractional operators
- References
- 2: Exploring numerical algorithms for fractional model solutions
- Abstract
- 2.1. Discretization of fractional integrals
- 2.2. Discretization of fractional derivatives
- 2.3. Product-integration rules for Caputo fractional problems
- 2.4. An explicit technique for a Caputo–Fabrizio Cauchy problem
- 2.5. A trapezoidal-based technique for the Caputo–Fabrizio problem
- 2.6. A trapezoidal-based technique the AB–Cauchy problem
- 2.7. A discretization of the time fractal-fractional models
- 2.8. A survey on numerical methods for fractal-fractional models
- 2.9. An efficient numerical approach for fractional diffusion PDEs
- References
- 3: Analytical methods for solving fractional differential equations
- Abstract
- 3.1. Solving the resonant Davey–Stewartson system using the M-fractional derivative
- 3.2. Solving the generalized Schrödinger's equation using the β-fractional derivative
- 3.3. Solving the third-order generalized Schrödinger equation using the conformable fractional derivative
- 3.4. On analytical solutions to a new integrable nonlinear Schrödinger equation via local fractal calculus
- References
- 4: Elucidating chaos in dynamical systems via fractional calculus
- Abstract
- 4.1. Dynamics of fractional-order chaotic systems
- 4.2. Applications of chaos indicators in fractional dynamics systems
- 4.3. On the chaotic systems including the fractal-fractional derivative
- References
- 5: Fractional frameworks for mathematical biology
- Abstract
- 5.1. Mathematical models of phytoplankton dynamics
- 5.2. A survey on fractional prey–predator models
- 5.3. Disease modeling using fractional differential equations
- 5.4. A review on epidemic models in sight of fractional calculus
- References
- 6: Fractional calculus perspective on noise removal in images
- Abstract
- 6.1. Fractional denoising masks for Gaussian noise
- 6.2. Some performance metrics in image processing
- 6.3. A generalized approach to fractional masks
- 6.4. Fractional masks using Prabhakar fractional calculus
- 6.5. Applications of adaptive strategies in fractional image processing
- 6.6. Fractional denoising masks for salt-and-pepper noise
- References
- 7: Novel fractional calculus based approaches for edge detection
- Abstract
- 7.1. Some fractional-based ideas in edge detection
- 7.2. The main results
- 7.3. Numerical experiments and discussions
- References
- 8: Some fractional calculus based approaches for image enhancement
- Abstract
- 8.1. Some mathematical background
- 8.2. The main materials
- References
- References
- References
- Index
- No. of pages: 302
- Language: English
- Edition: 1
- Published: June 21, 2024
- Imprint: Morgan Kaufmann
- Paperback ISBN: 9780443315008
- eBook ISBN: 9780443315015
BG
Behzad Ghanbari
Dr. Behzad Ghanbari is an associate professor of applied mathematics at Kermanshah University of Technology (KUT), Kermanshah, Iran. With a strong academic foundation, he earned his Bachelor’s, Master’s, and Doctoral degrees in applied mathematics in 2006, 2008, and 2012.
Dr. Ghanbari’s research is highly interdisciplinary, encompassing topics such as numerical analysis, numerical methods for solving partial and ordinary differential equations, fractional calculus, image processing, and related areas. His outstanding achievements have earned him recognition as one of the top young mathematicians in Iran. In 2021, he was honored with the highest research award in basic science from the Iranian Ministry of Science, Research, and Technology. Throughout his career, Dr. Ghanbari has published over 130 papers in prominent international journals and has been recognized as one of the top 1% scientists in the world in the field of Mathematics by Clarivate’s ESI since 2021 until now. His research has had a significant impact, with over 6,147 Scopus citations to date.
Affiliations and expertise
Associate Professor of Applied Mathematics at Kermanshah University of Technology (KUT), Kermanshah, IranRead Fractional Calculus on ScienceDirect