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Recent Developments in Theory and Applications of Fractional Order Systems

  • Book

  • February 2025
  • Elsevier Science and Technology
  • ID: 5994672

Recent Developments in Theory and Applications of Fractional Order Systems presents a rigorous and thorough analysis of various aspects of Fractional Calculus. The book provides readers with a thorough understanding of fundamental concepts and methods of applied mathematics utilized in a variety of scientific and engineering disciplines. The authors present each computational modeling concept with a definition, methods, theorems, and observations followed by typical application problems and step-by-step solutions. Each topic is covered in detail, followed typically by several meticulously worked out examples and a problem set containing many additional related problems. In addition, the book discusses recent developments and the latest research on Fractional Calculus and its applications, demonstrating important applications in Engineering, Computer Science, Management, Social Science, and the Humanities.

Table of Contents

1. Special Functions of the Fractional Calculus
2. Fractional Derivatives and Integrals
3. Transforms of Fractional Derivatives
4. Linear Fractional Differential Equations
5. Fractional Green's Function
6. Other Methods for the Solution of Fractional-order Equations
7. Fractional ordinary differential equations and properties
8. Existence and uniqueness of solutions to Cauchy-type problems
9. Stability estimates for fractional order differential equations
10. Partial Fractional differential equations and their solutions
11. Numerical Evaluation of Fractional Derivative
12. Approximation of Fractional Derivatives
13. Numerical method for fractional order ordinary differential equations
14. Finite-difference method for fractional ODEs
15. High-order approximation of Caputo fractional derivative
16. Adaptive and high-order scheme for non-integer order differential equations
17. Time-fractional diffusion equations
18. Fractional diffusion
19. Fractional-order Modeling
20. Linear Fractional-order Systems
21. Current trends in fractional derivatives
22. Fractional-order Control
23. Fractional integral inequalities and Applications
24. Discrete fractional calculus and applications
25. Fractional variational calculus and fractional Euler-Lagrange Equation
26. Fractional Calculus in Image/Signal Processing

Authors

Mehmet Yavuz Associate Professor, Department of Mathematics and Computer Sciences, Faculty of Science, Necmettin Erbakan University, Konya, Turkey. Dr. Mehmet Yavuz received his Ph.D. degree in Applied Mathematics from Balikesir University, Turkey. He conducted postdoctoral research in the Department of Mathematics at the University of Exeter, U.K., in 2019-2020. He is currently an Associate Professor in the Mathematics and Computer Sciences Department at Necmettin Erbakan University, Turkey. He has published more than 70 research papers in reputed journals and 60 conference papers as well as 6 book chapters in international books. He is the Editor of Fractional Calculus: New Applications in Understanding Nonlinear Phenomena, Bentham Books. His research interests include fractional calculus and its applications to the different fields of science, mathematical biology, nonlinear dynamics, and optimal control. Apart from being an Associate Editor of several esteemed journals, he is the Editor-in-Chief of Mathematical Modelling and Numerical Simulation with Applications. Dharmendra Kumar Singh Assistant Professor, Department of Mathematics, School of Basic Sciences, UIET, Chhatrapati Shahu Ji Maharaj University, Kanpur, India. Dr. Dharmendra Kumar Singh is an Assistant Professor in the Department of Mathematics, School of Basic Sciences, UIET, Chhatrapati Sahau Ji Maharaja University, Kanpur, India. His research interest is in Special functions, fractional calculus, partial fractional differential equations, and distribution theory. Dr. Singh received the A.K. Agarwal prize for best publication from The Society for Special Functions and Their Applications. Stuart Townley Centre for Environmental Mathematics, Faculty of Environment, Science and Economy, University of Exeter, UK. Dr. Stuart Townley is particularly interested research involving dynamical systems and control: the study of things (mechanical, biological, electrical, etc.) which interact and evolve in time and can be predicted, managed, and optimized. Dr. Townley has been the Chair in Applied Mathematics at the Environment and Sustainability Institute of the University of Exeter since June 2011. He works closely with colleagues in the College of Engineering, Mathematics and Physical Sciences, as well as in the College of Life and Environmental Sciences, to understand natural and man-made systems. Dr. Townley is also a member of the Mathematics Department in the College of Engineering, Mathematics and Physical Sciences, University of Exeter. He has previously held the positions of Chair in Applied Mathematics, Head of Department in the School of Mathematics, and Associate Dean in the Postgraduate Faculty at the University of Exeter.