Applied Mathematics in Science and Engineering,
Journal Year:
2024,
Volume and Issue:
32(1)
Published: April 2, 2024
This
study
delves
into
the
application
of
min-max
fuzzy
relation
systems,
specifically
focusing
on
equality
and
inequality,
in
examination
educational
institution
networks
their
resource-sharing
dynamics,
akin
to
a
P2P
network
structure.
Expanding
upon
this
framework,
article
intricately
explores
mathematical
system
featuring
three
or
more
terminals
within
an
education
resource
system,
each
comprising
distinct
sharing
capabilities.
The
exchange
information
various
facets,
encompassing
variations
expenditures
per
share
data,
framework
programming-type
objective
function,
constrained
by
parameters
system.
In
these
scenarios,
transfer
resources
from
one
terminal
another
is
interlinked,
introducing
complexities
that
warrant
comprehensive
examination.
Notably,
consideration
greater
downloading
specific
cases
proposed
for
enhanced
practicality.
primary
minimize
congestion
different
networks,
given
fixed
priority
grades
assigned
terminals.
To
achieve
this,
concept
Lexicographic
minimum
solution
introduced
address
max-min
inequalities,
aligning
with
defined
objectives.
presents
detailed
effective
scenario
implementing
minimal
solution.
For
validation
purposes,
supported
illustrative
examples,
offering
tangible
insights
its
applicability
efficacy.
Fractals,
Journal Year:
2023,
Volume and Issue:
31(05)
Published: Jan. 1, 2023
In
this
study,
we
proposed
a
novel
approach
for
modeling
the
dynamics
of
three-agent
financial
bubble
using
fractal-fractional
(FF)
derivative
Caputo
sense.
This
new
concept
was
developed
to
deal
with
complex
geometry
any
dynamical
system,
and
it
utilizes
both
fractional
order
fractal
term
independent
variables.
The
model
investigated
conformable
operator,
focus
on
dimension
order.
existence
uniqueness
solution
were
tested
FF
global
derivative,
approximate
root
system
calculated
numerically
iterative
technique
Newton
polynomial.
To
verify
accuracy
scheme,
applied
power
singular
law
two
parameters
in
numerical
technique.
curve
representation
also
verified
by
applying
data
fractals
different
orders.
Additionally,
sensitivities
varying
parameter
values.
allowed
us
gain
better
understanding
how
changes
these
affect
system’s
behavior
stability.
As
result,
study
presents
an
innovative
effective
bubbles
results
research
contribute
ongoing
efforts
develop
more
accurate
comprehensive
models
systems
economics
finance.
Fractals,
Journal Year:
2023,
Volume and Issue:
31(08)
Published: Jan. 1, 2023
In
this
paper,
we
study
the
existence
of
numerical
solution
and
stability
a
chemostat
model
under
fractal-fractional
order
derivative.
First,
investigate
positivity
roundedness
considered
system.
Second,
find
system
by
employing
Banach
Schauder
fixed-point
theorems.
Furthermore,
obtain
sufficient
condition
that
allows
stabling
solutions
using
numerical-functional
analysis.
We
proposed
exists
as
unique
positive
obeys
criteria
Ulam–Hyers
(U-H)
generalized
U-H
stability.
also
establish
analysis
for
scheme
based
on
Lagrange
interpolation
procedure.
Finally,
provide
two
examples
to
verify
correctness
theoretical
results.
remark
structure
described
is
sometimes
called
side
capacity
or
cross-flow
model.
The
here
can
be
seen
limiting
case
pattern
chemostats
in
parallel
with
diffusion
connection.
Moreover,
said
forms
natural
engineered
systems
significantly
affect
hydrodynamics
porous
media.
Fractal
calculus
an
excellent
tool
discuss
fractal
characteristics
media
characteristic
method
Results in Physics,
Journal Year:
2023,
Volume and Issue:
47, P. 106341 - 106341
Published: March 6, 2023
In
this
work,
a
multivariate
bilinear
neural
network
method
is
proposed
to
seek
more
exact
analytical
solutions
of
nonlinear
partial
differential
equations.
As
an
example,
the
(2+1)-dimensional
fractional
generalized
Calogero–Bogoyavlensky–Schiff–Bogoyavlensky–Konopelchenko
equation
investigated
via
selecting
3-2-2-1,
3-2-3-1
and
3-3-2-1
models,
respectively.
The
with
several
arbitrary
activation
functions
are
derived
dynamics
properties
shown
in
some
three-dimensional
density
maps
by
choosing
different
functions.
AIMS Mathematics,
Journal Year:
2024,
Volume and Issue:
9(6), P. 16116 - 16145
Published: Jan. 1, 2024
<abstract><p>This
research
focuses
on
the
fascinating
exploration
of
$
(2+1)
$-dimensional
complex
modified
Korteweg-de
Vries
(CmKdV)
system,
exhibiting
its
dynamics
and
solitary
wave
solutions.
This
system
is
a
versatile
mathematical
model
that
finds
applications
in
various
branches
physics,
including
fluid
dynamics,
plasma
optics,
nonlinear
dynamics.
Two
newly
developed
methodologies,
namely
auxiliary
equation
(AE)
method
Hirota
bilinear
(HB)
method,
are
implemented
for
construction
novel
solitons
formats.
Numerous
soliton
solutions
synthesised
distinct
formats,
such
as
dark,
bright,
singular,
periodic,
combo,
W
$-shape,
mixed
trigonometric,
exponential,
hyperbolic,
rational,
based
proposed
methods.
Furthermore,
we
also
find
some
lump
solutions,
periodic
cross
rational
wave,
homoclinic
breather
solution,
M
$-shaped
interaction
with
one
kink
multiwave
which
not
documented
literature.
In
addition,
employ
Galilean
transformation
to
derive
dynamic
framework
presented
equation.
Our
inquiry
includes
wide
range
topics,
bifurcations,
chaotic
flows,
other
intriguing
properties.
Also,
physical
demonstration
acquired
3D,
2D,
contour
plots
provided.
The
resulting
structure
results
can
enrich
dynamical
behaviors
given
may
be
useful
many
domains,
physics
well
demonstrate
approaches
used
effective
worthy
validation.</p></abstract>
Results in Physics,
Journal Year:
2024,
Volume and Issue:
58, P. 107432 - 107432
Published: Feb. 6, 2024
This
manuscript
is
a
captivating
exploration
of
the
(3+1)-D
nonlinear
extended
Quantum
Zakharov-Kuznetsov
(NLEQZK)
equation,
revealing
its
complex
dynamics
and
solitary
wave
solutions.
We
unveil
general
method
behind
this
equation
transform
it
into
an
ordinary
differential
(ODE),
then
venture
further
by
using
Galilean
transformation
to
create
system
ODEs.
Further,
we
journey
through
bifurcations,
chaos,
other
fascinating
dynamical
properties,
culminating
in
visualization
analysis
From
elegant
W-shaped
solitons
singular
with
unconventional
characteristics
hybrid
periodic
solitons,
each
discussed
vivid
detail.
work
presents
significant
advancement
understanding
unpredictable
intricate
behavior
model,
inviting
readers
explore
world
non-linear
waves
systems.
