Fractional 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.
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Table of Contents
1. Introduction to Fractional Calculus2. Exploring Numerical Algorithms for Fractional Model Solutions
3. Analytical methods for solving fractional differential equations
4. Elucidating Chaos in Dynamical Systems via Fractional Calculus
5. Fractional Frameworks for Mathematical Biology
6. Fractional Calculus Perspective on Noise Removal in Images
7. Novel Fractional Calculus Based Approaches for Edge Detection
8. Some Fractional Calculus Based Approaches for Image Enhancement
Authors
Behzad Ghanbari Professor of Applied Mathematics at Kermanshah University of Technology (KUT), Kermanshah, Iran.Dr. Behzad Ghanbari is a 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.
