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Fractional Calculus - Applications (Hardcover)
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Fractional Calculus - Applications (Hardcover)
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After presenting the first volume of this two-volume book,
presenting a lot of mathematical and theoretical studies and
research related to non-integer calculus, the second volume
illustrates applications related to this domain. This volume is
made up of 11 chapters. The first chapter presents the heuristic
power of the non-integer differential operators in physics starting
from the chaos to the emergence, the auto-organizations and the
holistic rules. The second chapter shows the dynamics of the
fractional order chaotic systems along with some applications. The
third chapter represents the pressure control of gas engines by
non-integer order controllers by showing a novel trend in the
application of the fractional calculus to automotive systems.
Chapter 4 shows the way to model fractional order equations using
state space modeling along with some applications. Another
application related to this domain is the thermal diffusive
interface. Chapter 5 shows the analysis of a semi-infinite diffuse
plane medium along with the equations that model this medium, and
some frequency and time domain responses. However, Chapter 6 treats
this problem by controlling this plant using the well-known CRONE
controller. Chapter 8 presents the adaptive second-order fractional
sliding mode control with an application to a water tanks level
system. Chapter 9 treats the mechanical aspect by showing the
features of the fractional operators applied to this domain. Also,
Chapter Nine presents the theory of diffusive stresses based on the
fractional advection-diffusion equation. The modeling of drug
diffusion during general anesthesia using Fractional Calculus is
shown in Chapter 10 and is considered as another application
related to the biomedical field. Finally, Chapter 11 represents an
overview of the fractional fuzzy controllers by showing the
analysis, the synthesis and the implementation of this module. To
sum up, this second volume presents applications of fractional
calculus in several engineering domains as the thermal, the
automotive, the mechanical, the biomedical and much more. Note that
this volume was preceded by a first volume that focuses on the
mathematical and theoretical aspects of fractional calculus.
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