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Recent Developments in Theory and Applications of Fractional Order Systems

  • 1st Edition - August 11, 2025
  • Latest edition
  • Editors: Mehmet Yavuz, Dharmendra Kumar Singh, Stuart Townley
  • Language: English

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… Read more

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Description

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.

Key features

  • Provides readers with a thorough understanding of fundamental concepts and methods of applied mathematics utilized in a variety of scientific and engineering disciplines
  • Presents a systematic introduction to most of the important special functions in Fractional Calculus that commonly arise in scientific and engineering practice
  • Explores many salient computational modeling properties
  • Analyzes theoretical and practical problems in Fractional Calculus in fields such as Engineering, Computer Science, Management, Social Science, and the Humanities

Readership

Researchers in computational modelling, applied mathematicians, and computer scientists working with researchers, engineers, and scientists in a wide range of modelling applications, Other interested audiences will be comprised of researchers, developers, and graduate students in computer science and mathematics interested in fractional calculus, including fractional differential equations, fractional optimal control problems, fractional kinetic equations, and fractional free electron laser equations

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

Product details

  • Edition: 1
  • Latest edition
  • Published: August 11, 2025
  • Language: English

About the editors

MY

Mehmet Yavuz

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.
Affiliations and expertise
Associate Professor, Department of Mathematics and Computer Sciences, Faculty of Science, Necmettin Erbakan University, Konya, Turkey

DS

Dharmendra Kumar Singh

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.
Affiliations and expertise
Assistant Professor, Department of Mathematics, School of Basic Sciences, UIET, Chhatrapati Shahu Ji Maharaj University, Kanpur, India

ST

Stuart Townley

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.
Affiliations and expertise
Centre for Environmental Mathematics, Faculty of Environment, Science and Economy, University of Exeter, UK

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