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.
General
Imprint: |
Academic Press Inc
|
Country of origin: |
United States |
Release date: |
March 2024 |
First published: |
2024 |
Editors: |
Snehashish Chakraverty
• Rajarama Mohan Jena
|
Dimensions: |
235 x 191mm (L x W) |
Pages: |
250 |
ISBN-13: |
978-0-443-15404-1 |
Categories: |
Books
|
LSN: |
0-443-15404-X |
Barcode: |
9780443154041 |
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