Computers in Biology and Medicine,
Journal Year:
2023,
Volume and Issue:
167, P. 107679 - 107679
Published: Nov. 8, 2023
We
present
a
novel
Pharmacokinetic/Pharmacodynamic
(PK/PD)
model
for
the
induction
phase
of
anesthesia,
incorporating
$\psi$-Caputo
fractional
derivative.
By
employing
Picard
iterative
process,
we
derive
solution
nonhomogeneous
system
to
characterize
dynamical
behavior
drugs
distribution
within
patient's
body
during
anesthesia
process.
To
explore
dynamics
model,
perform
numerical
analysis
on
solutions
involving
various
functions
$\psi$
and
orders.
All
simulations
are
conducted
using
MATLAB
computing
environment.
Our
results
suggest
that
order
differentiation
have
an
important
role
in
modeling
individual-specific
characteristics,
taking
into
account
complex
interplay
between
drug
concentration
its
effect
human
body.
This
innovative
serves
advance
understanding
personalized
responses
paving
way
more
precise
tailored
approaches
anesthetic
administration.
Fractal and Fractional,
Journal Year:
2023,
Volume and Issue:
7(8), P. 637 - 637
Published: Aug. 21, 2023
Sequential
minimal
optimization
(SMO)
method
is
an
algorithm
for
solving
problems
arising
from
the
training
process
of
support
vector
machines
(SVM).
The
SMO
mainly
used
to
solve
problem
objective
function
SVM,
and
it
can
have
high
accuracy.
However,
its
accuracy
be
improved.
Fractional
order
calculus
extension
integer
calculus,
which
more
accurately
describe
actual
system
get
accurate
results.
In
this
paper,
fractional
sequential
(FOSMO)
proposed
based
on
classification.
Firstly,
expressed
by
a
using
FOSMO
method.
representation
meaning
terms
in
are
studied.
Then
derivative
Lagrange
multipliers
obtained
according
calculus.
Lastly,
optimized
multipliers,
then
some
experiments
carried
out
linear
nonlinear
classification
cases.
Some
two-classification
multi-classification
situations,
experimental
results
show
that
obtain
better
than
normal
Partial Differential Equations in Applied Mathematics,
Journal Year:
2023,
Volume and Issue:
8, P. 100589 - 100589
Published: Nov. 23, 2023
The
goal
of
this
work
is
to
derive
and
study
a
new
model
which
traduces
the
transmission
dynamics
Buruli
ulcer
(BU),
in
we
replace
mass
action
incidences
with
standard
incidences,
consider
latent
period,
by
using
both
integer
fractional
derivatives.
We
first
present
reported
data
Cameroon
between
01/01/2001
31/12/2014,
statistical
that
approximates
real
as
closely
possible,
thus
make
forecasting
next
sixteen
years.
After
that,
formulate
Susceptible
humans-Exposed
humans-Infectious
humans-
Recovered
humans-Susceptible
humans;
vectors-Infectious
vectors
(SEIRS-SI)
type
compartmental
Ulcer
derivative.
compute
basic
reproduction
number
denoted
R0
prove
asymptotic
stability
Buruli-free
equilibrium
whenever
R0<1.
Then,
for
R0>1,
existence
an
unique
endemic
point
its
global
general
theory
Lyapunov.
perform
parameter
estimation
calibrate
our
from
Cameroon,
while
sensitivity
analysis
conducted
determine
important
parameters
BU
dynamics.
From
calibration,
obtain
R0=2.0843
greater
than
one
implies
country.
To
whether
if
or
not
admits
multiple
waves,
strength
A0.
find
A0≈17>0
means
Bu
epidemic
waves.
then
derivative
Caputo
Asymptotic
points
are
also
performed
model.
This
follows
proof
uniqueness
solutions
construct
numerical
scheme
based
on
Adams–Bashforth-Moulton
(ABM)
Method.
Theoretical
results
validated
simulations.
These
last
permits
evaluate
impact
varying
order
α
conclude
α<1,
cases
closer
prediction.
Contemporary Mathematics,
Journal Year:
2024,
Volume and Issue:
unknown, P. 2693 - 2708
Published: July 30, 2024
The
Formable
integral
transform
for
the
Hilfer-Prabhakar
and
Prabhakar
fractional
derivatives,
as
well
their
regularised
forms,
are
derived
in
this
article.
We
solve
several
Cauchy-type
differential
equations
with
derivatives
by
applying
Fourier
transformations
entirety,
including
three-parameter
Mittag-Leffler
function.
With
help
of
analytical
solutions
improved
comprehension
complicated
equations,
work
expands
use
transforms
calculus
across
a
range
scientific
engineering
fields.
Partial Differential Equations in Applied Mathematics,
Journal Year:
2024,
Volume and Issue:
11, P. 100853 - 100853
Published: Aug. 3, 2024
In
the
current
research
work,
classical
wave
equation
is
combined
with
a
nonlinear
sinh
source
term
in
sinh-Gordon
equation.
It
has
been
used
several
scientific
domains
such
as
differential
geometry
theory,
integrable
quantum
field
kink
dynamics,
and
statistical
mechanics.
makes
more
comprehensible
dynamics
of
strings
multi-strings
constant
curvature
space.
The
study
three
main
objectives.
Examine
governing
model
to
get
novel
solutions
by
employing
modified
Kudryashov
technique.
Then
compare
it
numerical
technique
variational
iteration
method
(MVIM)
calculate
error
terms.
Furthermore,
bifurcation
theory
produce
dynamical
system.
Additionally,
use
system's
sensitivity
analysis
investigate
model's
sensitivity.
At
last,
for
validation
acquired
results,
cryptography
image
encryption
decryption
used.
greatly
enhanced
presentation
thorough
2D
3D
phase
portraits.
mathematics
other
sciences
will
benefit
from
these
discoveries.
Contemporary Mathematics,
Journal Year:
2024,
Volume and Issue:
unknown, P. 3434 - 3461
Published: Aug. 23, 2024
This
paper
focuses
on
the
existence
and
uniqueness
of
solutions
for
a
new
class
coupled
fractional
differential
equations
subject
to
specific
boundary
conditions.
We
introduce
novel
approach
that
incorporates
(k,
ψ)-Hilfer
derivative,
recent
advancement
in
calculus.
By
leveraging
properties
this
operator,
we
develop
comprehensive
framework
analyze
proposed
system.
Our
findings,
established
through
application
Schauder's
fixed
point
theorem
Banach
contraction
principle,
contribute
understanding
complex
phenomena
modeled
by
equations.
research
expands
boundaries
calculus
offers
potential
applications
various
scientific
engineering
domains.
