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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Real analysis
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Fractional Calculus: Models And Numerical Methods (Hardcover)
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Fractional Calculus: Models And Numerical Methods (Hardcover)
Series: Series on Complexity, Nonlinearity, and Chaos, 3
Expected to ship within 10 - 15 working days
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The subject of fractional calculus and its applications (that is,
convolution-type pseudo-differential operators including integrals
and derivatives of any arbitrary real or complex order) has gained
considerable popularity and importance during the past three
decades or so, mainly due to its applications in diverse fields of
science and engineering. These operators have been used to model
problems with anomalous dynamics, however, they also are an
effective tool as filters and controllers, and they can be applied
to write complicated functions in terms of fractional integrals or
derivatives of elementary functions, and so on.This book will give
readers the possibility of finding very important mathematical
tools for working with fractional models and solving fractional
differential equations, such as a generalization of Stirling
numbers in the framework of fractional calculus and a set of
efficient numerical methods. Moreover, we will introduce some
applied topics, in particular fractional variational methods which
are used in physics, engineering or economics. We will also discuss
the relationship between semi-Markov continuous-time random walks
and the space-time fractional diffusion equation, which generalizes
the usual theory relating random walks to the diffusion equation.
These methods can be applied in finance, to model tick-by-tick
(log)-price fluctuations, in insurance theory, to study ruin, as
well as in macroeconomics as prototypical growth models.All these
topics are complementary to what is dealt with in existing books on
fractional calculus and its applications. This book was written
with a trade-off in mind between full mathematical rigor and the
needs of readers coming from different applied areas of science and
engineering. In particular, the numerical methods listed in the
book are presented in a readily accessible way that immediately
allows the readers to implement them on a computer in a programming
language of their choice. Numerical code is also provided.
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