The
objective
of the
workshop
is to
unite
the
separate
communities
of
fractional
calculus
and
nonlocal
calculus,
allowing
the
participants
to
explore
differences
and
similarities
between
them. A
central
goal is
to
gather
together
senior
and
junior
researchers
conducting
leading
research
on
nonlocal
models
to
exchange
their
recent
progress
and
results
and to
propose
future
research
guidelines.
The
workshop
will
include
a
poster
session
by young
researchers
(students,
postdocs,
assistant
professors).
Submit
abstracts
to:
mdelia@sandia.gov.
Abstract
submission
deadline:
September
15th,
2017
Notification
of
acceptance:
October
15th,
2017
Talks
are by
invitation
only,
but we
encourage
anyone
who is
interested
in the
topic to
participate.
Funds
are
available
for
young
researchers
and
young
minorities
(not
necessarily
already
engaged
in
nonlocal
research).
Early
registration
deadline:
October
30th,
2017
Link to
registration
will be
provided
soon.
The
organizers,
Marta
D'Elia,
Sandia
National
Laboratories
George
Em
Karniadakis,
Brown
University
The 18th
Congress
of the
U.S.
National
Committee
on
Theoretical
and
Applied
Mechanics
(USNC/TAM)
will be
hosted
by
Northwestern
University,
at the
Hyatt
Regency
O’Hare,
June 5 -
9, 2018.
This
Congress
is held
every
four
years
under
the
auspices
of the
USNC/TAM.
The
purpose
of the
Congress
is to
foster
and
promote
the
exchange
of ideas
and
information
among
the
various
disciplines
of the
TAM
community
around
the
world,
and to
chart
future
priorities
in
mechanics
related
research,
applications
and
education.
For the
first
time,
the
Congress
will be
jointly
organized
with the
Chinese
counterpart
organization,
the
Chinese
Society
of
Theoretical
and
Applied
Mechanics
(CS/TAM).
More
than
1,000
scholars
around
the
world
are
expected
to
attend
the
Congress.
Here is
the link
to the
Congress
website:
http://sites.northwestern.edu/usnctam2018/usnctam-2018/.
We
cordially
invite
you to
attend
the
minisymposium
"Fractional
Differential
Equations:
Experiments,
Analyses,
Algorithms
and
Applications"
(with
reference
number
#101).
A
description
of this
minisymposium
is
attached
below.
Please
submit
online
before
November
10,
2017.
If
there is
any
problem
or
suggestions,
please
feel
free to
contact
any of
us.
Recent
years
have
witnessed
growing
interest
and
expanding
applications
of
fractional
calculus
in real
world
problems.
This
minisymposium
aims
to create synergies
among researchers
from mechanics,
mathematics,
materials/environmental sciences, and
scientific
computing.
Topics
of
particular
interest
include
but are
not
limited
to:
# Modeling
with
fractional
differential
equations/fractional
calculus,
e.g.,
for
materials
and
transport
processes
# Fractional
differential
equations
for
model
reduction
with
experimental
or
computational
data
# Algorithms
and
numerical
studies
of
fractional
differential
equations
# Mathematical
analyses
of
fractional
systems
# Stochastic
fractional
dynamic
systems
and
statistical
analysis
# Fractional
control
of
linear,
nonlinear
and
distributed-parameter
systems
This invaluable monograph is devoted to a rapidly developing area on the research of qualitative theory of fractional ordinary and partial differential equations. It provides the readers the necessary background material required to go further into the subject and explore the rich research literature. The tools used include many classical and modern nonlinear analysis methods such as fixed point theory, measure of noncompactness method, topological degree method, the technique of Picard operators, critical point theory and semigroup theory. Based on the research work carried out by the authors and other experts during the past seven years, the contents are very recent and comprehensive.
In this edition, two new topics have been added, that is, fractional impulsive differential equations, and fractional partial differential equations including fractional Navier–Stokes equations and fractional diffusion equations.
More information on this book can be found by the following links:
Karabi Biswas, Gary Bohannan, Riccardo Caponetto, António
Lopes, J. A. Tenreiro Machado
Book Description
This book focuses on two specific areas related to fractional order systems – the realization of physical devices characterized by non-integer order impedance, usually called fractional-order elements (FOEs); and the characterization of vegetable tissues via electrical impedance spectroscopy (EIS) – and provides readers with new tools for designing new types of integrated circuits. The majority of the book addresses FOEs.
The interest in these topics is related to the need to produce “analogue” electronic devices characterized by non-integer order impedance, and to the characterization of natural phenomena, which are systems with memory or aftereffects and for which the fractional-order calculus tool is the ideal choice for analysis.
FOEs represent the building blocks for designing and realizing analogue integrated electronic circuits, which the authors believe hold the potential for a wealth of mass-market applications. The freedom to choose either an integer- or non-integer-order analogue integrator/derivator is a new one for electronic circuit designers. The book shows how specific non-integer-order impedance elements can be created using materials with specific structural properties.
EIS measures the electrical impedance of a specimen across a given range of frequencies, producing a spectrum that represents the variation of the impedance versus frequency – a technique that has the advantage of avoiding aggressive examinations.
Biological tissues are complex systems characterized by dynamic processes that occur at different lengths and time scales; this book proposes a model for vegetable tissues that describes the behavior of such materials by considering the interactions among various relaxing phenomena and memory effects.
More information on this book can be found by the following links:
A governing equation of stable random walks is developed in one dimension. This Fokker-Planck equation is similar to, and contains as a subset, the second-order advection dispersion equation (ADE) except that the order (α) of the highest derivative is fractional (e.g., the 1.65th derivative). Fundamental solutions are Lévy's α-stable densities that resemble the Gaussian except that they spread proportional to time1/α, have heavier tails, and incorporate any degree of skewness. The measured variance of a plume undergoing Lévy motion would grow faster than Fickian plume, at a rate of time2/α, where 0 < α ≤ 2. The equation is parsimonious since the parameters are not functions of time or distance. The scaling behavior of plumes that undergo Lévy motion is accounted for by the fractional derivatives, which are appropriate measures of fractal functions. In real space the fractional derivatives are integrodifferential operators, so the fractional ADE describes a spatially nonlocal process that is ergodic and has analytic solutions for all time and space.
This paper proposes a new concept of random-order fractional differential equation model, in which a noise term is included in the fractional order. We investigate both a random-order anomalous relaxation model and a random-order time fractional anomalous diffusion model to demonstrate the advantages and the distinguishing features of the proposed models. From numerical simulation results, it is observed that the scale parameter and the frequency of the noise play a crucial role in the evolution behaviors of these systems. In addition, some potential applications of the new models are presented.