Computation and Modeling for Fractional Order Systems
- 1st Edition - February 20, 2024
- Imprint: Academic Press
- Editors: Snehashish Chakraverty, Rajarama Mohan Jena
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 3 - 1 5 4 0 4 - 1
- eBook ISBN:9 7 8 - 0 - 4 4 3 - 1 5 4 0 5 - 8
Computation and Modeling for Fractional Order Systems provides readers with problem-solving techniques for obtaining exact and/or approximate solutions of governing equations… Read more
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Computation and Modeling for Fractional Order Systems provides readers with problem-solving techniques for obtaining exact and/or approximate solutions of governing equations arising in fractional dynamical systems presented using various analytical, semi-analytical, and numerical methods. Various analytical/semi-analytical/numerical methods are applied for solving real-life fractional order problems. The comprehensive descriptions of different recently developed fractional singular, non-singular, fractal-fractional, and discrete fractional operators, along with computationally efficient methods, are included for the reader to understand how these may be applied to real-world systems, and a wide variety of dynamical systems such as deterministic, stochastic, continuous, and discrete are addressed.
Fractional calculus has gained increasing popularity and relevance over the last few decades, due to its well-established applications in various fields of science and engineering. It deals with the differential and integral operators with non-integral powers. Fractional differential equations are the pillar of various systems occurring in a wide range of science and engineering disciplines, namely physics, chemical engineering, mathematical biology, financial mathematics, structural mechanics, control theory, circuit analysis, and biomechanics, among others.
- Includes the most recent and up-to-date developments in the theory and scientific applications of Fractional Order Systems, including a wide variety of real-world applications
- Provides an integrated and complete overview of key topics in Fractional Order Systems, including computational efficient analytical and numerical methods, local fractional derivatives, variable order fractal-fractional models, piecewise concepts, fractional order integrodifferential models, uncertainty modeling and AI, nonlinear dynamics and chaos, and discrete fractional operator
- Presents readers with a comprehensive, foundational reference for this key topic in computational modeling, which is a mathematical underpinning for new areas of scientific and engineering research
mathematicians, researchers in computational modelling and computational biology, computer scientists, engineers, as well as researchers in biomedical engineering, control engineering, mechatronics, and robotics. May be used as a text for teaching classical and advanced fractional differential calculus to graduate students and researchers.
1: Computational Efficient Analytical and Numerical Methods for Fractional Order Models – Hamid M. Sedighi – H-index 33 – Shahid Chamran University, Ahvaz, Iran
1.1. Introduction
1.2. Preliminaries
1.3. Analytical methods
1.4. Numerical Methods
1.5. Semi-analytical methods
1.6. Few examples
1.7. Conclusion
2: Local Fractional Derivatives and Their Applications – Mehmet Yavuz – H-index 21 – University of Exeter, Cornwall UK
2.1. Introduction/Motivation
2.2. Concept of Local fractional derivatives
2.3. Mathematical Examples
2.4. Application problems
2.5. Conclusion
3: Variable Order Fractal-Fractional Models – Thabet Abdeljawad – H-index 50 – Prince Sultan University, Riyadh, Saudi Arabia
3.1. Introduction
3.2. Variable order fractal-fractional derivatives
3.3. Variable order fractal-fractional integrals
3.4. Model description
3.5. Numerical algorithm
3.6. Example problems
3.7. Conclusion
4: Piecewise Concept in Fractional Models – Waleed Adel – H-index 6 – Université Française d’Egypte and Rajarama Mohan Jena – H-index 13 – National Institute of Technology – Rourkela, India
4.1. Introduction
4.2. Piecewise derivative with global and classical types
4.3. Piecewise integral with global and classical types
4.4. Piecewise derivative with fractional derivatives
4.5. Piecewise derivative and integrals with singular and non-singular kernels
4.6. Numerical algorithms
4.7. Illustrative examples
4.8. Conclusion
5: Fractional Order Integrodifferential Models – Snehashish Chakraverty – H-index 32 – National Institute of Technology, Rourkela, India and Nihar Ranjan Mallick - H-index 0 – National Institute of Technology, Rourkela, India (co-author is a graduate assistant to Dr. Chakraverty)
5.1. Introduction
5.2. Integrodifferential equations
5.3. Integrodifferential equations of fractional order
5.4. Numerical methods
5.5. Convergence analysis
5.6. Numerical examples
5.7. Conclusion
6: Uncertainty Modelling and AI in Fractional Models – Snehashish Chakraverty – H-index 32 – National Institute of Technology, Rourkela, India, Kasimala Narasimha Rao, and Arup K. Sahoo – H-index 0 - National Institute of Technology, Rourkela, India (co-authors are graduate assistants to Dr. Chakraverty)
6.1. Introduction
6.2. Preliminaries of uncertainty and AI
6.3. Fractional models in uncertain environment
6.4. Machine Intelligence in fractional models
6.5. Numerical results
6.6. Conclusion
7: Fractional Calculus in Epidemiology, Biomathematics, and Financial Mathematics – Sunday O. Edeki – H-index 16 - Covenant University – Ota, Nigeria
7.1. Introduction
7.2. Formulation of dynamical models related to the said title
7.3. Existence and uniqueness of the solution
7.4. Stability analysis
7.5. Numerical method
7.6. Error analysis
7.7. Result and discussion
7.8. Conclusion
8: Nonlinear Dynamics and Chaos in Science and Engineering – Shengda Zeng – H-index – 22 – Uniwersytet Jagielloński, Krakow, Poland
8.1. Introduction
8.2. Formulation of the model
8.3. Existence and uniqueness
8.4. Stability analysis
8.5. Chaotic study
8.6. Numerical method
8.7. Result and discussion
8.8. Conclusion
9: Discrete Fractional Operators with Applications – Hadi Rezazadeh – H-index 38 – Amol University of Special Modern Technologies, Amol, Iran
9.1. Introduction
9.2. Concept of discrete fractional operators
9.3. Model formulation
9.4. Numerical method
9.5. Result and discussion
9.6. Conclusion
10: New Fractional Operators in Real-Life Dynamical Models – Dumitru Baleanu – H-index 94 – Cankaya Universitesi, Ankara, Turkey
10.1. Motivation of using new fractional operators
10.2. Preliminaries
10.3. Description of real-life dynamical model
10.4. Existence and uniqueness
10.5. Stability analysis
10.6. Numerical algorithm
10.7. Result and discussion
10.8. Conclusion
11: Application of Fractional Calculus in Electrical, Chemical, and Mechanical Engineering – Snehashish Chakraverty – H-index 32 – National Institute of Technology, Rourkela, India and Shweta Dubey – H-index 0 - National Institute of Technology, Rourkela, India (co-author is a graduate assistant to Dr. Chakraverty)
11.1. Introduction
11.2. Description of fractional models arise in electrical, chemical and mechanical engineering
11.3. Method description
11.4. Existence, uniqueness, and stability analysis
11.5. Result and discussion
11.6. Conclusion
1.1. Introduction
1.2. Preliminaries
1.3. Analytical methods
1.4. Numerical Methods
1.5. Semi-analytical methods
1.6. Few examples
1.7. Conclusion
2: Local Fractional Derivatives and Their Applications – Mehmet Yavuz – H-index 21 – University of Exeter, Cornwall UK
2.1. Introduction/Motivation
2.2. Concept of Local fractional derivatives
2.3. Mathematical Examples
2.4. Application problems
2.5. Conclusion
3: Variable Order Fractal-Fractional Models – Thabet Abdeljawad – H-index 50 – Prince Sultan University, Riyadh, Saudi Arabia
3.1. Introduction
3.2. Variable order fractal-fractional derivatives
3.3. Variable order fractal-fractional integrals
3.4. Model description
3.5. Numerical algorithm
3.6. Example problems
3.7. Conclusion
4: Piecewise Concept in Fractional Models – Waleed Adel – H-index 6 – Université Française d’Egypte and Rajarama Mohan Jena – H-index 13 – National Institute of Technology – Rourkela, India
4.1. Introduction
4.2. Piecewise derivative with global and classical types
4.3. Piecewise integral with global and classical types
4.4. Piecewise derivative with fractional derivatives
4.5. Piecewise derivative and integrals with singular and non-singular kernels
4.6. Numerical algorithms
4.7. Illustrative examples
4.8. Conclusion
5: Fractional Order Integrodifferential Models – Snehashish Chakraverty – H-index 32 – National Institute of Technology, Rourkela, India and Nihar Ranjan Mallick - H-index 0 – National Institute of Technology, Rourkela, India (co-author is a graduate assistant to Dr. Chakraverty)
5.1. Introduction
5.2. Integrodifferential equations
5.3. Integrodifferential equations of fractional order
5.4. Numerical methods
5.5. Convergence analysis
5.6. Numerical examples
5.7. Conclusion
6: Uncertainty Modelling and AI in Fractional Models – Snehashish Chakraverty – H-index 32 – National Institute of Technology, Rourkela, India, Kasimala Narasimha Rao, and Arup K. Sahoo – H-index 0 - National Institute of Technology, Rourkela, India (co-authors are graduate assistants to Dr. Chakraverty)
6.1. Introduction
6.2. Preliminaries of uncertainty and AI
6.3. Fractional models in uncertain environment
6.4. Machine Intelligence in fractional models
6.5. Numerical results
6.6. Conclusion
7: Fractional Calculus in Epidemiology, Biomathematics, and Financial Mathematics – Sunday O. Edeki – H-index 16 - Covenant University – Ota, Nigeria
7.1. Introduction
7.2. Formulation of dynamical models related to the said title
7.3. Existence and uniqueness of the solution
7.4. Stability analysis
7.5. Numerical method
7.6. Error analysis
7.7. Result and discussion
7.8. Conclusion
8: Nonlinear Dynamics and Chaos in Science and Engineering – Shengda Zeng – H-index – 22 – Uniwersytet Jagielloński, Krakow, Poland
8.1. Introduction
8.2. Formulation of the model
8.3. Existence and uniqueness
8.4. Stability analysis
8.5. Chaotic study
8.6. Numerical method
8.7. Result and discussion
8.8. Conclusion
9: Discrete Fractional Operators with Applications – Hadi Rezazadeh – H-index 38 – Amol University of Special Modern Technologies, Amol, Iran
9.1. Introduction
9.2. Concept of discrete fractional operators
9.3. Model formulation
9.4. Numerical method
9.5. Result and discussion
9.6. Conclusion
10: New Fractional Operators in Real-Life Dynamical Models – Dumitru Baleanu – H-index 94 – Cankaya Universitesi, Ankara, Turkey
10.1. Motivation of using new fractional operators
10.2. Preliminaries
10.3. Description of real-life dynamical model
10.4. Existence and uniqueness
10.5. Stability analysis
10.6. Numerical algorithm
10.7. Result and discussion
10.8. Conclusion
11: Application of Fractional Calculus in Electrical, Chemical, and Mechanical Engineering – Snehashish Chakraverty – H-index 32 – National Institute of Technology, Rourkela, India and Shweta Dubey – H-index 0 - National Institute of Technology, Rourkela, India (co-author is a graduate assistant to Dr. Chakraverty)
11.1. Introduction
11.2. Description of fractional models arise in electrical, chemical and mechanical engineering
11.3. Method description
11.4. Existence, uniqueness, and stability analysis
11.5. Result and discussion
11.6. Conclusion
- Edition: 1
- Published: February 20, 2024
- Imprint: Academic Press
- Language: English
SC
Snehashish Chakraverty
Dr. Snehashish Chakraverty is a Senior Professor in the Department of Mathematics (Applied Mathematics Group), National Institute of Technology Rourkela, with over 30 years of teaching and research experience. A gold medalist from the University of Roorkee (now IIT Roorkee), he earned his Ph.D. from IIT Roorkee and completed post-doctoral work at the University of Southampton (UK) and Concordia University (Canada). He has also served as a visiting professor in Canada and South Africa. Dr. Chakraverty has authored/edited 38 books and published over 495 research papers. His research spans differential equations (ordinary, partial, fractional), numerical and computational methods, structural and fluid dynamics, uncertainty modeling, and soft computing techniques. He has guided 27 Ph.D. scholars, with 10 currently under his supervision.
He has led 16 funded research projects and hosted international researchers through prestigious fellowships. Recognized in the top 2% of scientists globally (Stanford-Elsevier list, 2020–2024), he has received numerous awards including the CSIR Young Scientist Award, BOYSCAST Fellowship, INSA Bilateral Exchange, and IOP Top Cited Paper Awards. He is Chief Editor of International Journal of Fuzzy Computation and Modelling and serves on several international editorial boards.
Affiliations and expertise
HAG Professor, Department of Mathematics, Applied Mathematics Group, National Institute of Technology Rourkela, Rourkela, Odisha, India. Differential Equations (ordinary, partial, and fractional), Numerical Analysis, Computational Methods, Structural Dynamics (FGM, Nano), Fluid Dynamics, Mathematical and Uncertainty Modelling, Soft Computing and Machine Intelligence (Artificial Neural Network, Fuzzy, Interval, and Affine Computations).RJ
Rajarama Mohan Jena
Rajarama Mohan Jena is Senior Research Fellow in the Department of Mathematics (Applied Mathematics Group) at the National Institute of Technology Rourkela, Odisha, India. He has an M.Sc. in Applied Mathematics and Computing from the Indian Institute of Technology, Dhanbad, India. Rajarama’s area of research interest includes Fractional Calculus, Partial Differential Equations, Numerical Analysis, Mathematical Modelling, and Uncertainty Modelling, and he has been assisting Dr. Chakraverty in various research projects relating to this book.
Affiliations and expertise
Senior Research Fellow, Department of Mathematics (MA), National Institute of Technology Rourkela, IndiaRead Computation and Modeling for Fractional Order Systems on ScienceDirect