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This invaluable monograph is devoted to a rapidly developing area
on the research of qualitative theory of fractional ordinary and
partial differential equations. It provides the readers the
necessary background material required to go further into the
subject and explore the rich research literature. The tools used
include many classical and modern nonlinear analysis methods such
as fixed point theory, measure of noncompactness method,
topological degree method, the technique of Picard operators,
critical point theory and semigroup theory. Based on the research
work carried out by the authors and other experts during the past
seven years, the contents are very recent and comprehensive.In this
edition, two new topics have been added, that is, fractional
impulsive differential equations, and fractional partial
differential equations including fractional Navier-Stokes equations
and fractional diffusion equations.
Stability and Controls Analysis for Delay Systems is devoted to
stability, controllability and iterative learning control (ILC) to
delay systems, including first order system, oscillating systems,
impulsive systems, fractional systems, difference systems and
stochastic systems raised from physics, biology, population
dynamics, ecology and economics, currently not presented in other
books on conventional fields. Delayed exponential matrix function
approach is widely used to derive the representation and stability
of the solutions and the controllability. ILC design are also
established, which can be regarded as a way to find the control
function. The broad variety of achieved results with rigorous
proofs and many numerical examples make this book unique.
This book extends classical Hermite-Hadamard type inequalities to
the fractional case via establishing fractional integral
identities, and discusses Riemann-Liouville and Hadamard integrals,
respectively, by various convex functions. Illustrating theoretical
results via applications in special means of real numbers, it is an
essential reference for applied mathematicians and engineers
working with fractional calculus. Contents Introduction
Preliminaries Fractional integral identities Hermite-Hadamard
inequalities involving Riemann-Liouville fractional integrals
Hermite-Hadamard inequalities involving Hadamard fractional
integrals
This book presents fractional difference, integral, differential,
evolution equations and inclusions, and discusses existence and
asymptotic behavior of their solutions. Controllability and relaxed
control results are obtained. Combining rigorous deduction with
abundant examples, it is of interest to nonlinear science
researchers using fractional equations as a tool, and physicists,
mechanics researchers and engineers studying relevant topics.
Contents Fractional Difference Equations Fractional Integral
Equations Fractional Differential Equations Fractional Evolution
Equations: Continued Fractional Differential Inclusions
This book introduces iterative learning control (ILC) and its
applications to the new equations such as fractional order
equations, impulsive equations, delay equations, and multi-agent
systems, which have not been presented in other books on
conventional fields. ILC is an important branch of intelligent
control, which is applicable to robotics, process control, and
biological systems. The fractional version of ILC updating laws and
formation control are presented in this book. ILC design for
impulsive equations and inclusions are also established. The broad
variety of achieved results with rigorous proofs and many numerical
examples make this book unique. This book is useful for graduate
students studying ILC involving fractional derivatives and
impulsive conditions as well as for researchers working in pure and
applied mathematics, physics, mechanics, engineering, biology, and
related disciplines.
This book introduces iterative learning control (ILC) and its
applications to the new equations such as fractional order
equations, impulsive equations, delay equations, and multi-agent
systems, which have not been presented in other books on
conventional fields. ILC is an important branch of intelligent
control, which is applicable to robotics, process control, and
biological systems. The fractional version of ILC updating laws and
formation control are presented in this book. ILC design for
impulsive equations and inclusions are also established. The broad
variety of achieved results with rigorous proofs and many numerical
examples make this book unique. This book is useful for graduate
students studying ILC involving fractional derivatives and
impulsive conditions as well as for researchers working in pure and
applied mathematics, physics, mechanics, engineering, biology, and
related disciplines.
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