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Theory and Applications of Fractional Differential Equations, Volume 204 (Hardcover, 204th edition)
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Theory and Applications of Fractional Differential Equations, Volume 204 (Hardcover, 204th edition)
Series: North-Holland Mathematics Studies
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This monograph provides the most recent and up-to-date developments
on fractional differential and fractional integro-differential
equations involving many different potentially useful operators of
fractional calculus.
The subject of fractional calculus and its applications (that is,
calculus of integrals and derivatives of any arbitrary real or
complex order) has gained considerable popularity and importance
during the past three decades or so, due mainly to its demonstrated
applications in numerous seemingly diverse and widespread fields of
science and engineering.
Some of the areas of present-day applications of fractional models
include Fluid Flow, Solute Transport or Dynamical Processes in
Self-Similar and Porous Structures, Diffusive Transport akin to
Diffusion, Material Viscoelastic Theory, Electromagnetic Theory,
Dynamics of Earthquakes, Control Theory of Dynamical Systems,
Optics and Signal Processing, Bio-Sciences, Economics, Geology,
Astrophysics, Probability and Statistics, Chemical Physics, and so
on.
In the above-mentioned areas, there are phenomena with estrange
kinetics which have a microscopic complex behaviour, and their
macroscopic dynamics can not be characterized by classical
derivative models.
The fractional modelling is an emergent tool which use fractional
differential equations including derivatives of fractional order,
that is, we can speak about a derivative of order 1/3, or square
root of 2, and so on. Some of such fractional models can have
solutions which are non-differentiable but continuous functions,
such as Weierstrass type functions. Such kinds of properties are,
obviously, impossible for the ordinary models.
What are the useful properties of these fractional operators which
help in the modelling of so many anomalous processes? From the
point of view of the authors and from known experimental results,
most of the processes associated with complex systems have
non-local dynamics involving long-memory in time, and the
fractional integral and fractional derivative operators do have
some of those characteristics.
This book is written primarily for the graduate students and
researchers in many different disciplines in the mathematical,
physical, engineering and so many others sciences, who are
interested not only in learning about the various mathematical
tools and techniques used in the theory and widespread applications
of fractional differential equations, but also in further
investigations which emerge naturally from (or which are motivated
substantially by) the physical situations modelled mathematically
in the book.
This monograph consists of a total of eight chapters and a very
extensive bibliography. The main objective of it is to complement
the contents of the other books dedicated to the study and the
applications of fractional differential equations. The aim of the
book is to present, in a systematic manner, results including the
existence and uniqueness of solutions for the Cauchy type problems
involving nonlinear ordinary fractional differential equations,
explicit solutions of linear differential equations and of the
corresponding initial-value problems through different methods,
closed-form solutions of ordinary and partial differential
equations, and a theory of the so-called sequential linear
fractional differential equations including a generalization of the
classical Frobenius method, and also to include an interesting set
of applications of the developed theory.
Key features:
- It is mainly application oriented.
- It contains a complete theory of Fractional Differential
Equations.
- It can be used as a postgraduate-level textbook in many different
disciplines within science and engineering.
- It contains an up-to-date bibliography.
- It provides problems and directions for further
investigations.
- Fractional Modelling is an emergent tool with demonstrated
applications in numerous seemingly diverse and widespread fields of
science and engineering.
- It contains many examples.
- and so on
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