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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. 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.
The aim of this book is to handle different application problems of
science and engineering using expert Artificial Neural Network
(ANN). As such, the book starts with basics of ANN along with
different mathematical preliminaries with respect to algebraic
equations. Then it addresses ANN based methods for solving
different algebraic equations viz. polynomial equations,
diophantine equations, transcendental equations, system of linear
and nonlinear equations, eigenvalue problems etc. which are the
basic equations to handle the application problems mentioned in the
content of the book. Although there exist various methods to handle
these problems, but sometimes those may be problem dependent and
may fail to give a converge solution with particular
discretization. Accordingly, ANN based methods have been addressed
here to solve these problems. Detail ANN architecture with step by
step procedure and algorithm have been included. Different example
problems are solved with respect to various application and
mathematical problems. Convergence plots and/or convergence tables
of the solutions are depicted to show the efficacy of these
methods. It is worth mentioning that various application problems
viz. Bakery problem, Power electronics applications, Pole
placement, Electrical Network Analysis, Structural engineering
problem etc. have been solved using the ANN based methods.
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Wave Dynamics (Hardcover)
Snehashish Chakraverty, Perumandla Karunakar
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R2,719
Discovery Miles 27 190
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Ships in 10 - 15 working days
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There are various types of waves including water, sound,
electromagnetic, seismic and shock etc. These waves need to be
analyzed and understood for different practical applications. This
book is an attempt to consider the waves in detail to understand
the physical and mathematical phenomena. A major challenge is to
model waves by experimental studies.The aim of this book is to
address the efficient and recently developed theories along with
the basic equations of wave dynamics. The latest development of
analytical/semi analytical and numerical methods with respect to
wave dynamics are also covered. Further few challenging
experimental studies are considered for related problems. This book
presents advances in wave dynamics in simple and easy to follow
chapters for the benefit of the readers/researchers.
Plates are integral parts of most engineering structures and their
vibration analysis is required for safe design. Vibration of Plates
provides a comprehensive, self-contained introduction to vibration
theory and analysis of two-dimensional plates. Reflecting the
author's more than 15 years of original research on plate
vibration, this book presents new methodologies and demonstrates
their effectiveness by providing comprehensive results. The text
also offers background information on vibration problems along with
a discussion of various plate geometries and boundary conditions,
including the new concepts of Boundary Characteristic Orthogonal
Polynomials (BCOPs).
This book will deal with different sections associated with
bending, buckling and vibration of nanobeams and nanoplates along
with systematic description of handling the complexities when
nanoscales are considered. The introduction includes basic ideas
concerned with nanostructures, the algorithms and iterations
followed in numerical methods and introduction to beam and plate
theories in conjunction with nonlocal elasticity theory applied in
nanostructures.Next, the investigation of nanobeams and nanoplates
subjected to different sets of boundary conditions based on various
nonlocal theories will be included. The varieties of physical and
geometrical parameters that influence the bending, buckling and
vibration mechanisms will be summarized.Finally, effect of
environments such as thermal environment, Winkler-Pasternak elastic
foundations and non-uniformity etc. on the buckling and vibration
mechanisms will be illustrated.
This book addresses the basics of interval/fuzzy set theory,
artificial neural networks (ANN) and computational methods. It
presents step-by-step modeling for application problems along with
simulation and numerical solutions. In general, every science and
engineering problem is inherently biased by uncertainty, and there
is often a need to model, solve and interpret problems in the world
of uncertainty. At the same time, exact information about models
and parameters of practical applications is usually not known and
precise values do not exist. This book discusses uncertainty in
both data and models. It consists of seven chapters covering
various aspects of fuzzy uncertainty in application problems, such
as shallow water wave equations, static structural problems,
robotics, radon diffusion in soil, risk of invasive alien species
and air quality quantification. These problems are handled by means
of advanced computational and fuzzy theory along with machine
intelligence when the uncertainties involved are fuzzy. The
proposed computational methods offer new fuzzy computing methods
that help other areas of knowledge construction where inexact
information is present.
This book addresses the basics of interval/fuzzy set theory,
artificial neural networks (ANN) and computational methods. It
presents step-by-step modeling for application problems along with
simulation and numerical solutions. In general, every science and
engineering problem is inherently biased by uncertainty, and there
is often a need to model, solve and interpret problems in the world
of uncertainty. At the same time, exact information about models
and parameters of practical applications is usually not known and
precise values do not exist. This book discusses uncertainty in
both data and models. It consists of seven chapters covering
various aspects of fuzzy uncertainty in application problems, such
as shallow water wave equations, static structural problems,
robotics, radon diffusion in soil, risk of invasive alien species
and air quality quantification. These problems are handled by means
of advanced computational and fuzzy theory along with machine
intelligence when the uncertainties involved are fuzzy. The
proposed computational methods offer new fuzzy computing methods
that help other areas of knowledge construction where inexact
information is present.
Computational Structural Mechanics: Static and Dynamic Behaviors
provides a cutting-edge treatment of functionally graded materials
and the computational methods and solutions of FG static and
vibration problems of plates. Using the Rayleigh-Ritz method,
static and dynamic problems related to behavior of FG rectangular,
Levy, elliptic, skew and annular plates are discussed in detail. A
thorough review of the latest research results, computational
methods and applications of FG technology make this an essential
resource for researchers in academia and industry.
Interval Finite Element Method with MATLAB provides a thorough
introduction to an effective way of investigating problems
involving uncertainty using computational modeling. The well-known
and versatile Finite Element Method (FEM) is combined with the
concept of interval uncertainties to develop the Interval Finite
Element Method (IFEM). An interval or stochastic environment in
parameters and variables is used in place of crisp ones to make the
governing equations interval, thereby allowing modeling of the
problem. The concept of interval uncertainties is systematically
explained. Several examples are explored with IFEM using MATLAB on
topics like spring mass, bar, truss and frame.
This book contains select chapters on support vector algorithms
from different perspectives, including mathematical background,
properties of various kernel functions, and several applications.
The main focus of this book is on orthogonal kernel functions, and
the properties of the classical kernel functions-Chebyshev,
Legendre, Gegenbauer, and Jacobi-are reviewed in some chapters.
Moreover, the fractional form of these kernel functions is
introduced in the same chapters, and for ease of use for these
kernel functions, a tutorial on a Python package named ORSVM is
presented. The book also exhibits a variety of applications for
support vector algorithms, and in addition to the classification,
these algorithms along with the introduced kernel functions are
utilized for solving ordinary, partial, integro, and fractional
differential equations. On the other hand, nowadays, the real-time
and big data applications of support vector algorithms are growing.
Consequently, the Compute Unified Device Architecture (CUDA)
parallelizing the procedure of support vector algorithms based on
orthogonal kernel functions is presented. The book sheds light on
how to use support vector algorithms based on orthogonal kernel
functions in different situations and gives a significant
perspective to all machine learning and scientific machine learning
researchers all around the world to utilize fractional orthogonal
kernel functions in their pattern recognition or scientific
computing problems.
The subject of fractional calculus has gained considerable
popularity and importance during the past three decades, mainly due
to its validated applications in various fields of science and
engineering. It is a generalization of ordinary differentiation and
integration to arbitrary (non-integer) order. The fractional
derivative has been used in various physical problems, such as
frequency-dependent damping behavior of structures, biological
systems, motion of a plate in a Newtonian fluid, controller for the
control of dynamical systems, and so on. It is challenging to
obtain the solution (both analytical and numerical) of related
nonlinear partial differential equations of fractional order. So
for the last few decades, a great deal of attention has been
directed towards the solution for these kind of problems. Different
methods have been developed by other researchers to analyze the
above problems with respect to crisp (exact) parameters. However,
in real-life applications such as for biological problems, it is
not always possible to get exact values of the associated
parameters due to errors in measurements/experiments, observations,
and many other errors. Therefore, the associated parameters and
variables may be considered uncertain. Here, the uncertainties are
considered interval/fuzzy. Therefore, the development of
appropriate efficient methods and their use in solving the
mentioned uncertain problems are the recent challenge. In view of
the above, this book is a new attempt to rigorously present a
variety of fuzzy (and interval) time-fractional dynamical models
with respect to different biological systems using computationally
efficient method. The authors believe this book will be helpful to
undergraduates, graduates, researchers, industry, faculties, and
others throughout the globe.
Vibration of Functionally Graded Beams and Plates uses numerically
efficient computational techniques to analyze vibration problems
associated with FG beams and plates. Introductory material on FG
materials and structural members, as well as a range of vibration
and shear deformation theories are discussed, providing a valuable
summary of these broader themes. The latest research and analysis
of vibration in FG materials is presented in an
application-oriented manner, linking the research to its importance
in fields such as aerospace, nuclear power, and automotive
engineering. The book also features research on the complicating
effects of thermal environments, piezoelectricity, and elastic
foundations. The innovative computational procedures and simulation
results are shown in full throughout, providing a uniquely valuable
resource for users of numerical modeling software. This book is
essential reading for any researcher or practitioner interested in
FG materials, or the design of technology for the nuclear power,
aerospace, and automotive industries.
This book discusses soft computing, which provides an efficient
platform to deal with imprecision, uncertainty, vagueness and
approximation in order to attain robustness and reliable computing.
It explores two major concepts of soft computing: fuzzy set theory
and neural networks, which relate to uncertainty handling and
machine learning techniques respectively. Generally, fuzzy sets are
considered as vague or uncertain sets having membership function
lying between 0 and 1, and ANN is a type of artificial intelligence
that attempts to imitate the way a human brain works by configuring
specific applications, for instance pattern recognition or data
classification, through learning processes. The book also presents
C/MATLAB programming codes related to the basics of fuzzy set,
interval arithmetic and ANN in a concise, practical and adaptable
manner along, with simple examples and self-validation unsolved
practice questions in few cases
In general, every problem of science and engineering is governed by
mathematical models. There is often a need to model, solve and
interpret the problems one encounters in the world of practical
problems. Models of practical application problems usually need to
be handled by efficient computational models. New Paradigms in
Computational Modeling and Its Applications deals with recent
developments in mathematical methods, including theoretical models
as well as applied science and engineering. The book focuses on
subjects that can benefit from mathematical methods with concepts
of simulation, waves, dynamics, uncertainty, machine intelligence,
and applied mathematics. The authors bring together leading-edge
research on mathematics combining various fields of science and
engineering. This perspective acknowledges the inherent
characteristic of current research on mathematics operating in
parallel over different subject fields. New Paradigms in
Computational Modeling and Its Applications meets the present and
future needs for the interaction between various science and
technology/engineering areas on the one hand and different branches
of mathematics on the other. As such, the book contains 13 chapters
covering various aspects of computational modeling from theoretical
to application problems. The first six chapters address various
problems of structural and fluid dynamics. The next four chapters
include solving problems where the governing parameters are
uncertain regarding fuzzy, interval, and affine. The final three
chapters will be devoted to the use of machine intelligence in
artificial neural networks.
Plates are integral parts of most engineering structures and their
vibration analysis is required for safe design. Vibration of Plates
provides a comprehensive, self-contained introduction to vibration
theory and analysis of two-dimensional plates. Reflecting the
author's more than 15 years of original research on plate
vibration, this book presents new methodologies and demonstrates
their effectiveness by providing comprehensive results. The text
also offers background information on vibration problems along with
a discussion of various plate geometries and boundary conditions,
including the new concepts of Boundary Characteristic Orthogonal
Polynomials (BCOPs).
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