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The main subject of the monograph is the fractional calculus in the
discrete version. The volume is divided into three main parts. Part
one contains a theoretical introduction to the classical and
fractional-order discrete calculus where the fundamental role is
played by the backward difference and sum. In the second part,
selected applications of the discrete fractional calculus in the
discrete system control theory are presented. In the discrete
system identification, analysis and synthesis, one can consider
integer or fractional models based on the fractional-order
difference equations. The third part of the book is devoted to
digital image processing.
This book touches upon various aspects of a very interesting, and
growing in popularity category of models of dynamical systems.
These are the so-called fractional-order systems. Such models are
not only relevant for many fields of science and technology, but
may also find numerous applications in other disciplines applying
the mathematical modelling tools. Thus, the book is intended for a
very wide audience of professionals who want to expand their
knowledge of systems modelling and its applications. The book
includes the selections of papers presented at the International
Conference on Fractional Calculus and its Applications organized by
the Warsaw University of Technology and was held online on 6-8
September 2021. The International Conference on Fractional Calculus
and its Applications (ICFDA) has an almost twenty years history. It
started in Bordeaux (France) in 2004, followed by Porto (Portugal)
2006, Istanbul (Turkey) 2008, Badajoz (Spain) 2010, Nanjing (China)
2012, Catania (Italy) 2014, Novi Sad (Serbia) 2016, Amman (Jordan)
2018. Next ICFDA was planned in 2020 in Warsaw (Poland), but
COVID-19 pandemic shifted it to 6-8 September 2021. Hence, the
organizers were forced to change the form of the conference to the
online one. In the volume twenty eight high-quality research papers
presented during the ICFDA 2021 eleven Regular Sessions with an
additional online Discussion Session are presented. The presented
papers are scientifically inspiring, leading to new fruitful ideas.
They cover a very broad range of many disciplines. Nowadays, and
especially in such a subject as fractional calculus, it is very
difficult to assign papers to specific scientific areas. So, many
of the papers included have an interdisciplinary character.
This book focuses on fractional calculus, presenting novel advances
in both the theory and applications of non-integer order systems.
At the end of the twentieth century it was predicted that it would
be the calculus of the twenty-first century, and that prophecy is
confirmed year after year. Now this mathematical tool is
successfully used in a variety of research areas, like engineering
(e.g. electrical, mechanical, chemical), dynamical systems
modeling, analysis and synthesis (e.g technical, biological,
economical) as well as in multidisciplinary areas (e.g.
biochemistry, electrochemistry).As well as the mathematical
foundations the book concentrates on the technical applications of
continuous-time and discrete-time fractional calculus,
investigating the identification, analysis and control of
electrical circuits and dynamical systems. It also presents the
latest results.Although some scientific centers and scientists are
skeptical and actively criticize the applicability of fractional
calculus, it is worth breaking through the scientific and
technological walls. Because the "fractional community" is growing
rapidly there is a pressing need for the exchange of scientific
results. The book includes papers presented at the 9th
International Conference on Non-integer Order Calculus and Its
Applications and is divided into three parts:* Mathematical
foundations* Fractional systems analysis and synthesis* System
modelingSeven papers discuss the mathematical foundations, twelve
papers address fractional order analysis and synthesis and three
focus on dynamical system modeling by the fractional order
differential and difference equations. It is a useful resource for
fractional calculus scientific community.
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