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In the nineteenth-century, fractional calculus had its origin in
extending differentiation and integration operators from the
integer-order case to the fractional-order case. Discrete
fractional calculus has recently become an important research
topic, useful in various science and engineering applications. The
first definition of the fractional-order discrete-time/difference
operator was introduced in 1974 by Diaz and Osler, where such
operator was derived by discretizing the fractional-order
continuous-time operator. Successfully, several types of
fractional-order difference operators have then been proposed and
introduced through further generalizing numerous classical
operators, motivating several researchers to publish extensively on
a new class of systems, viz the nonlinear fractional-order
discrete-time systems (or simply, the fractional-order maps), and
their chaotic behaviors. This discovery of chaos in such maps, has
led to novel control methods for effectively stabilizing their
chaotic dynamics.The aims of this book are as follows:
The book reports on the latest advances in and applications of
fractional order control and synchronization of chaotic systems,
explaining the concepts involved in a clear, matter-of-fact style.
It consists of 30 original contributions written by eminent
scientists and active researchers in the field that address
theories, methods and applications in a number of research areas
related to fractional order control and synchronization of chaotic
systems, such as: fractional chaotic systems, hyperchaotic systems,
complex systems, fractional order discrete chaotic systems, chaos
control, chaos synchronization, jerk circuits, fractional chaotic
systems with hidden attractors, neural network, fuzzy logic
controllers, behavioral modeling, robust and adaptive control,
sliding mode control, different types of synchronization, circuit
realization of chaotic systems, etc. In addition to providing
readers extensive information on chaos fundamentals, fractional
calculus, fractional differential equations, fractional control and
stability, the book also discusses key applications of fractional
order chaotic systems, as well as multidisciplinary solutions
developed via control modeling. As such, it offers the perfect
reference guide for graduate students, researchers and
practitioners in the areas of fractional order control systems and
fractional order chaotic systems.
The book reports on the latest advances in and applications of
fractional order control and synchronization of chaotic systems,
explaining the concepts involved in a clear, matter-of-fact style.
It consists of 30 original contributions written by eminent
scientists and active researchers in the field that address
theories, methods and applications in a number of research areas
related to fractional order control and synchronization of chaotic
systems, such as: fractional chaotic systems, hyperchaotic systems,
complex systems, fractional order discrete chaotic systems, chaos
control, chaos synchronization, jerk circuits, fractional chaotic
systems with hidden attractors, neural network, fuzzy logic
controllers, behavioral modeling, robust and adaptive control,
sliding mode control, different types of synchronization, circuit
realization of chaotic systems, etc. In addition to providing
readers extensive information on chaos fundamentals, fractional
calculus, fractional differential equations, fractional control and
stability, the book also discusses key applications of fractional
order chaotic systems, as well as multidisciplinary solutions
developed via control modeling. As such, it offers the perfect
reference guide for graduate students, researchers and
practitioners in the areas of fractional order control systems and
fractional order chaotic systems.
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