Results in Physics,
Journal Year:
2023,
Volume and Issue:
55, P. 107161 - 107161
Published: Nov. 4, 2023
In
this
study,
multi-term
time
fractional
2D
telegraph
type
equations,
as
a
new
category
of
differential
are
introduced.
The
orthonormal
Chelyshkov
polynomials
used
basis
functions
to
generate
collocation
method
for
such
equations.
way,
results
obtained
the
and
classical
derivatives
these
polynomials.
proposed
method,
by
representing
problem's
solution
in
terms
(with
unknown
coefficients)
applying
extracted
matrices,
along
with
is
elicited
problem
under
consideration.
fact,
finding
initial
turns
into
assigning
expansion
coefficients
through
solving
system
algebraic
accuracy
numerically
checked
several
examples.
Mathematical Methods in the Applied Sciences,
Journal Year:
2023,
Volume and Issue:
46(16), P. 17313 - 17327
Published: June 27, 2023
Continued
mortality
from
Covid‐19
disease
and
environmental
considerations
resulting
the
cemetery,
landfill,
wastewater
treatment
plants,
mass
personal
protective
equipment
(PPE)
disposal
sites
demonstrate
importance
of
carefully
studying
how
microorganisms
spread
in
across
soil,
surface
water,
groundwater.
In
this
research,
fractional
diffusion
equation
for
different
functions
has
been
solved
using
derivative
form
with
variable‐order
(VO)
to
predict
SARS‐CoV‐2
virus.
Comparison
obtained
results
available
experimental
data
mathematical
calculations
shows
that
use
VO
can
viral
behavior
more
accurately.
The
main
advantage
considering
a
derivatives
instead
constant‐order
or
classical
is
accurately
predicting
propagation
over
large
time
dimensional
scales.
addition,
specified
virus,
method
presented
study
will
be
able
investigate
pattern
all
pollutants
at
nanoscale/microscale,
including
carcinogenic
compounds,
such
as
biogenic
amines
aqueous
porous
media.
manifest
high
accuracy
approach
which
provides
helpful
information
urban
health
planners/managers
worldwide
manage
other
possible
outbreaks.
AIMS Mathematics,
Journal Year:
2024,
Volume and Issue:
9(5), P. 11560 - 11579
Published: Jan. 1, 2024
<abstract><p>In
this
study,
we
introduce
a
novel
framework
for
exploring
the
dynamics
of
tumor
growth
and
an
evolution
model
two-stage
carcinogenic
mutations
in
two-dimensions
based
on
system
reaction-diffusion
equations.
It
is
shown
theoretically
that
globally
stable
absence
both
delay
diffusion.
The
inclusion
diffusion
does
not
destabilize
system,
while
including
capture
key
elements
how
normal
cells
convert
into
cancer
cells.
To
further
validate
these
results,
several
numerical
experiments
are
performed
different
parameter
values
involved
equation.
These
chosen
sense
they
have
some
biological
meanings
using
steady
states
equilibrium
points.
For
purpose
simulation,
Euler
scheme
used
temporal
discretization,
Fourier
spectral
method
space
variables,
which
natural
choice
due
to
periodic
boundary
conditions
simulation
results
confirm
our
theoretical
justification.</p></abstract>
Journal of Biomaterials Science Polymer Edition,
Journal Year:
2024,
Volume and Issue:
35(13), P. 1978 - 1998
Published: July 2, 2024
Glioma
cancer
is
the
primary
cause
of
cancer-related
fatalities
globally
for
both
men
and
women.
Traditional
chemotherapy
treatments
this
condition
frequently
result
in
reduced
efficacy
significant
adverse
effects.
This
investigation
developed
a
new
drug
delivery
system
chemotherapeutic
temozolomide
(TMZ)
using
pH-sensitive
zeolitic
imidazolate
frameworks
(ZIF-8).
These
nanoplatforms
demonstrate
excellent
biocompatibility
hold
potential
therapy.
Utilizing
favorable
reaction
milieu
offered
by
ZIFs,
'one-pot
method'
was
employed
fabrication
loading
drugs,
leading
to
good
capacity
loading.
TMZ@TA@ZIF-8
NPs
exhibit
notable
response
an
acidic
milieu,
resulting
enhanced
release
pattern
characterized
controlled
outcome.
The
effectiveness
inhibiting
migration
invasion
U251
glioma
cells,
as
well
promoting
apoptosis,
confirmed
through
various
tests,
including
MTT
(3-(4,5)-dimethylthiahiazo(-z-y1))
assay,
DAPI/PI
dual
staining,
cell
scratch
assay.
biochemical
fluorescent
staining
assays
showed
that
potentially
improved
ROS,
MMP,
triggered
apoptosis
cells.
In
cells
treated
with
NPs,
p53,
Bax,
Cyt-C,
caspase-3,
-8,
-9
expressions
were
significantly
enhanced,
while
Bcl-2
expression
diminished.
outcomes
show
therapeutic
agent
anti-glioma
properties.
Overall,
pH-responsive
systems
we
fabricated
great
treatment.
approach
has
make
contributions
improvement
therapy
overcoming
problems
associated
TMZ-based
treatments.
Results in Physics,
Journal Year:
2023,
Volume and Issue:
53, P. 106937 - 106937
Published: Sept. 6, 2023
In
this
paper,
the
one-
and
two-dimensional
multi-order
time
fractional
telegraph
equations
are
introduced.
Two
collocation
methods
based
on
Romanovski–Jacobi
polynomials
proposed
to
solve
them.
way,
some
operational
matrices
related
classical
derivatives
of
these
achieved
at
first.
Then,
solution
problem
under
consideration
is
approximated
by
a
finite
expansion
with
unknown
coefficients.
Next,
an
algebraic
system
created
in
terms
coefficients
applying
derived
technique.
Eventually,
solving
determining
expressed
coefficients,
for
equation
obtained.
The
correctness
developed
schemes
checked
examples.
Deleted Journal,
Journal Year:
2023,
Volume and Issue:
47(5-6), P. 1649 - 1664
Published: Oct. 3, 2023
Hepatitis
B
is
the
most
common
serious
liver
infection
in
world.
The
cause
of
this
hepatitis
virus
(HBV)
that
attacks
cells
and
leads
to
injury.
This
work
aims
compute
an
approximate
solution
fractional
order
HBV
epidemic
model
(F-HBV-M)
by
use
optimization
method
on
base
a
new
basis
function,
generalized
Bessel
polynomials
(GBPs).
first
formulated
then
using
Caputo
derivative.
provides
form
GBPs.
To
solve
model,
Lagrange
multipliers
coupled
with
Analyzing
convergence,
we
finally
provide
accurate
numerical
graphical
descriptions
for
our
F-HBV-M
model.
