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Fractional Calculus - Theory (Hardcover)
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Fractional Calculus - Theory (Hardcover)
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The first volume of this two-volume book, presents history, the
mathematical modelling and the applications of fractional order
systems, and contains mathematical and theoretical studies and
research related to this domain. This volume is made up of 11
chapters. The first chapter presents an analysis of the Caputo
derivative and the pseudo state representation with the infinite
state approach. The second chapter studies the stability of a class
of fractional Cauchy problems. The third chapter shows how to solve
fractional order differential equations and fractional order
partial differential equations using modern matrix algebraic
approaches. Following this chapter, chapter four proposes another
analytical method to solve differential equations with local
fractional derivative operators. Concerning chapter five, it
presents the extended Borel transform and its related fractional
analysis. After presenting the analytical resolution methods for
fractional calculus, chapter six shows the essentials of fractional
calculus on discrete settings. The initialisation of such systems
is shown in chapter seven. In fact, this chapter presents a
generalised application of the Hankel operator for initialisation
of fractional order systems. The last four chapters show some new
studies and applications of non-integer calculus. In fact, chapter
eight presents the fractional reaction-transport equations and
evanescent continuous time random walks. Chapter nine shows a novel
approach in the exponential integrators for fractional differential
equations. Chapter ten presents the non-fragile tuning of
fractional order PD controllers for integrating time delay systems.
At the end, chapter eleven proposes a discrete finite-dimensional
approximation of linear infinite dimensional systems. To sum up,
this volume presents a mathematical and theoretical study of
fractional calculus along with a stability study and some
applications. This volume ends up with some new techniques and
methods applied in fractional calculus. This volume will be
followed up by a second volume that focuses on the applications of
fractional calculus in several engineering domains.
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