Computation and Modeling for Fractional Order Systems - Softcover

Softcover

ISBN 10: 044315404X ISBN 13: 9780443154041

Publisher: Academic Press, 2024

Synopsis

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

About this title

About the Authors

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.

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.

From the Back Cover

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. In this regard, this book brings together contemporary and computationally efficient methods for investigating real-world fractional order systems in one volume. 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. The fractional derivative has also been used in various other physical problems, such as frequency-dependent damping behavior of structures, motion of a plate in a Newtonian fluid, PID controller for the control of dynamical systems, and many others. The mathematical models in electromagnetics, rheology, viscoelasticity, electrochemistry, control theory, Brownian motion, signal and image processing, fluid dynamics, financial mathematics, and material science are well defined by fractional-order differential equations. Generally, these physical models are demonstrated either by ordinary or partial differential equations. However, modeling these problems by fractional differential equations, on the other hand, can make the physics of the systems more feasible and practical in some cases. In order to know the behavior of these systems, we need to study the solutions of the governing fractional models. The exact solution of fractional differential equations may not always be possible using known classical methods. Generally, the physical models occurring in nature comprise complex phenomena, and it is sometimes challenging to obtain the solution (both analytical and numerical) of nonlinear differential equations of fractional order. Various aspects of mathematical modeling that may include deterministic or uncertain (viz. fuzzy or interval or stochastic) scenarios along with fractional order (singular/non-singular kernels) are important to understand the dynamical systems. Computation and Modeling for Fractional Order Systems covers various types of fractional order models in deterministic and non-deterministic scenarios. 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 by the authors of the book.

Edition details

• Publisher: Academic Press
• Publication date: 2024
• Language: English
• ISBN 10: 044315404X
• ISBN 13: 9780443154041
• Binding: Paperback
• Edition number: 1
• Number of pages: 250
• Editor: Chakraverty Ph.D. Snehashish, Jena Rajarama Mohan