

Latest
Issue
Volume
15, No.
2,
June 2022
Articles 


Numerical
Solution of
FractionalOrder
Population
Growth Model
using
FractionalOrder
MuntzLegendre
Collocation
Method and
PadeApproximants
This paper
presents a
numerical
solution for
a nonlinear
fractional
Volterra
integrodifferential
equation to
study the
behavior
solution of
the
population
growth
model. The
technique
applied
based on the
fractionalorder
Muntz–Legendre
polynomials
and the Pade
approximants.
Finally,
some
numerical
examples are
presented to
show the
efficiency
and validity
of the
proposed
method. 

Elias Hengamian Asl
Jafar SaberiNadjafi
Morteza Gachpazan
JJMS,
2022, 15(2),
157175 
In
this
paper,
a
new
analogue
of
blossom
based
on
postquantum
calculus
is
introduced.
The
postquantum
blossom
has
been
adapted
for
developing
identities
and
algorithms
for
Bernstein
basis
and
Bezier
curves.
By
applying
the
postquantum
blossom,
various
new
identities
and
formulae
expressing
the
monomials
in
terms
of
the
postquantum
Bernstein
basis
and
a
postquantum
variant
of
Marsden’s
identity
are
investigated.
For
each
postquantum
Bezier
curves
of
degree
m, a
collection
of
m!
new,
affine
invariant,
recursive
evaluation
algorithms
are
derived.


Alaa
Mohammed
Obad
Khalid Khan
D. K.
Lobiyal
Asif Khan
JJMS,
2022, 15(2),
177197



Harina P.
Waghamore
Husna
Vallijan
Chao Meng
JJMS,
2022, 15(2),
199210

Numerical Solution of Bioheat Transfer Model using Generalized Wavelet Collocation Method
In this article, we develop a a generalized wavelet collocation method based on a Haar wavelet to facilitate the solution of modified Pennes bioheat transfer model during thermal therapy. The process of heat transfer in living biological tissue is studied under various coordinate systems. Contrary to the existing operational matrix methods based on orthogonal functions, we construct the Haar wavelet operational matrices of integration without using the block pulse functions. The temperature distribution inside a living biological tissue has been investigated for different estimations of thermal conductivity, antenna power constant, and surface temperature. The numerical results obtained shows that the desired temperature occur faster in spherical symmetric coordinate as compared to axisymmetric coordinate where as temperature in axisymmetric coordinate occur faster in comparison
to cartesian coordinate. The performance and accuracy of the proposed technique is elucidates by a comparison of the numerical outcomes with homotopy perturbation method and the exact solution of the model.


Mohd Irfan
Firdous A.
Shah
JJMS,
2022, 15(2),
211229

Frame Systems in NonLocally Convex Banach Spaces
In this paper, we define atomic decompositions in a non locally convex Banach space Ɩ^{p} (0 < p ≤ 1) and discuss its existence through examples. Also, a sufficient condition for its existence is given and it is observed that if a pBanach space has an atomic decomposition, then the space is isomorphic to its associated pBanach sequence space. Further, necessary and sufficient conditions for an atomic decomposition in a pBanach space is given. Finally, we define shrinking atomic decomposition and gave a necessary and sufficient condition for it.


N. P. Pahari
Teena Kohli
J. L.
Ghimire
JJMS,
2022, 15(2),
231242

On Star Coloring of Degree Splitting of Cartesian Product Graphs
A star coloring of a graph G is a proper vertex coloring with the condition that no path on four vertices in G can be labelled by two colors. The star chromatic number χs (G) of G is the least number of colors that is required to star color G. In this paper, we determine the star chromatic number of the degree splitting graph of the Cartesian product of any two simple graphs G and H denoted by G□H and also we portray the star chromatic number for the degree splitting graph of the Cartesian product of prism graphs, toroidal graphs and grid graphs.


S. Ulagammal
Vernold
Vivin J.
Ismail Naci
Cangul
JJMS,
2022, 15(2),
243254

Construction
of a Riesz
Wavelet
Basis on
Locally
Compact
Abelian
Groups
We have
explored the
concept of
Riesz
multiresolution
analysis on
a locally
compact
Abelian
group G, and
have
extensively
studied the
methods of
construction
of a Riesz
wavelet from
the given
Riesz MRA.
We have
proved that,
if δα is the
order of
dilation,
then
precisely δα−1
functions
are required
to construct
a Riesz
wavelet
basis for L^{2}
(G). An
example,
supporting
our theory
and
illustrating
the methods
developed,
has also
been
discussed in
detail. 

Satyapriya
Raj Kumar
JJMS,
2022, 15(2),
255274

A Study on
Fuzzy Weak
Enriched
Vector Soft
Topology
In this
paper, the
notions of
fuzzy
enriched
soft
topology,
fuzzy weak
enriched
soft
topology and
fuzzy weak
enriched
vector soft
topology are
introduced.
The relation
between
fuzzy vector
soft
topology and
fuzzy
enriched
soft
topology is
obtained. In
this
connection,
several
properties
are
discussed.
This paper
also
discusses
extensions
of ideas of
convexity
and balance
to the fuzzy
soft case. 

Bijan Davvaz
V. Madhuri
B.
Amudhambigai
JJMS,
2022, 15(2),
275290

On α − and α
*−
T_{0}
and T_{1}
Separation
Axioms In
I− Fuzzy
Topological
Spaces
Sostak and
Kubiak
introduced
I−fuzzy
topological
spaces.
Subspaces
and products
of I−fuzzy
topological
spaces have
been
introduced
and studied
by Peeters
and Sostak.
Srivastava
et al.
introduced
and studied
α− and α*−Hausdorff
I−fuzzy
topological
space.
George and
Veeramani
improved the
definition
of a fuzzy
metric,
which was
first
introduced
by Kramosil
and Michalek.
Grecova et
al.
constructed
an LM−fuzzy
topological
space using
a strong
fuzzy
metric,
where L
and M
are complete
sublattices
of the unit
interval
[0,1]
containing 0
and 1.
This LM−fuzzy
topological
space
reduces to
an I−
fuzzy
topological
space if L =
M = I = [0,
1]. In this
paper, we
have
introduced α
− T_{0},
α*
− T_{0},
α − T_{1}
and α*
− T_{1}
separation
axioms in
I−fuzzy
topological
spaces and
established
several
basic
desirable
results. In
particular,
it has been
proved that
these
separation
axioms
satisfy the
hereditary,
productive
and
projective
properties.
Further, we
have proved
that in an
I−fuzzy
topological
space, α−Hausdorff⇒
α − T_{1}
⇒ α − T_{0
}and α*−Hausdorff⇒
α*
− T_{1}
⇒ α*
− T_{0}.
It has been
also shown
that an I−fuzzy
topological
space
induced by a
strong fuzzy
metric is α−Hausdorff,
for α ∈ [0,
1) and α*−Hausdorff,
for α ∈ (0,
1], which
further
implies that
this I−fuzzy
topological
space
satisfies α
− T_{0},
α*
− T_{0},
α − T_{1}
and α*
− T_{1}
separation
axioms. 

Seema Mishra
JJMS,
2022, 15(2),
291307

On Maximal
Ideal Space
of the
Functionally
Countable
Subring of
C(F)
Let X be a
Tychonoff
space and F,
a filter
base of
dense
subsets of X
(i.e., it is
closed under
finite
intersection)
and let C(F)
= lim_{S∈F}
C(S), where
C(S) is the
ring of all
realvalued
continuous
functions on
S. It is
known that
C(F) =
□{C(S) : S ∈
F }. By C_{c}(F)
(C*_{c}(F)),
we mean a
subring of
C(F)
consisting
of (bounded)
functions
with
countable
range. In
this paper,
we study M_{c}
(M*_{c}),
the maximal
ideal space
of C_{c}(F)
(C*_{c}(F))
with the
hullkernel
topology.
Equivalent
topology for
each of them
provided. It
is shown
that both M_{c
}and M*_{c}
are T_{4}spaces.
More
generally,
they are
homeomorphic.
Particularly,
we prove
that the
maximal
ideal space
of Q_{c}(X)
(q_{c}(X))
and the
maximal
ideal space
of Q*_{c}(X)
(q*_{c}(X))
are
homeomorphic,
where Q_{c}(X)
(q_{c}(X))
is the
maximal
(classical)
ring of
quotients of
C_{c}(X),
and Q*_{c}(X)
(q*_{c}(X))
is the
subring
consisting
of bounded
functions.


Amir Veisi
JJMS,
2022, 15(2),
309324

Homoderivations
on a Lattice
In this
paper, the
concept of
homoderivation
on a lattice
as a
combination
of two
concepts of
meethomomorphisms
and
derivations
is
introduced.
Some
characterizations
and
properties
of
homoderivations
are
provided.
The
relationship
between
derivations
and
homoderivations
on a lattice
is
established.
Also, an
interesting
class of
homoderivations
namely
isotone
homoderivations
is studied.
A
characterization
of the
isotone
homoderivations
in terms of
the meethomomorphisms
is given.
Furthermore,
a sufficient
condition
for a
homoderivation
to become
isotonic is
established.


Mourad
Yettou
Abdelaziz
Amroune
JJMS,
2022, 15(2),
325338 
On Strongly
g(x)Invo
Clean Rings
In this
paper we
characterize
strongly
g(x)invo
clean rings
and specify
the relation
between
strongly
g(x)invo
clean rings
and strongly
clean rings.
Further,
some general
properties
and relevant
examples of
strongly
g(x)invo
clean rings
are
presented. 

Noor Abed
Alhaleem
A. Handam
A. Ahmad
JJMS,
2022, 15(2),
339347 
A Note on Generalized
Frame
Potential
The concept
of the frame
potential
was defined
by Benedetto
and Fickus
[1] and it
was showed
that the
finite unit
norm tight
frames can
be
characterized
as the
minimizers
of the the
energy
functional.
The concept
was
generalized
by Carrizo
and Heineken
[5] and they
introduced
the concept
of mixed
frame
potential.
In the
present
paper, we
further
generalize
the concept
introducing
the notion
of
generalized
frame
potential
and observe
that frame
potential
and mixed
frame
potential
are
particular
cases of
generalized
frame
potential.
We prove
some results
concerning
the
generalized
frame
potential. 

S. K. Sharma
Virender
JJMS,
2022, 15(2),
349362 
Solving
Conformable
Evolution
Equations by
an Extended
Numerical
Method
In this
paper, an
extension
for the tanhfunction
method is
proposed by
using an (α_{1},
α_{2},
..., α_{n},
β)− rational
transformation
method, n is
an arbitrary
integer. As
applications
and to
illustrate
the validity
of this
method, the
(1+3)
dimensional
conformable
time and
space
factional
Burgers
equation,
and two
other
(1+3)dimensional
conformable
fractional
evolution
examples,
that are
useful for
academic
purposes,
are solved.
More kink
and
generalized
traveling
wave
solutions
are obtained
and some
threedimensional
solution
graphs are
presented at
the end of
this paper.


Zoubir
Dahmani
Ahmed Anber
Iqbal Jebril
JJMS,
2022, 15(2),
363380







