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Characterizing semi-groups through the properties of their fuzzy \(m\)-bi-ideals
Characterizing semi-groups through the properties of their fuzzy \(m\)-bi-ideals
en
en
In this article, we present the idea of the fuzzy \(m\)-bi-ideals in semi-groups and describe their basic algebraic properties. We also develop the forms of the fuzzy \(m\)-bi-ideals generated by an element, a subset, and a sub-semi-group of the semi-group. Important characterizations of semi-groups and their different types like \(m\)-regular semi-groups and \(m\)-intraregular semi-groups have been given through demonstrating examples and using properties of fuzzy \(m\)-bi-ideals in semi-groups.
170
180
Mohammad
Munir
Department of Mathematics
Government Postgraduate College
Pakistan
dr.mohammadmunir@gmail.com
Nasreen
Kausar
Department of Mathematics and Statistics
University of Agriculture
Pakistan
kausar.nasreen57@gmail.com
Salahuddin
Department of Mathematics
Jazan University
Kingdom of Saudi Arabia
Anum
Shafiq
School of Mathematics and Statistics
Nanjing University of Information Science and Technology
China
Mustafa
Habib
Department of Mathematics
University of Engineering and Technology
Pakistan
Bipotency
Fuzzy \(m\)-points
\(m\)-regular semi-groups
\(m\)-intraregular semi-groups
Article.1.pdf
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]
Analysis of the dynamics of a mathematical model for HIV infection
Analysis of the dynamics of a mathematical model for HIV infection
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en
Mathematical models are essential tools in the study of different infectious diseases. Researchers have developed other in-host models to investigate HIV dynamics in the human body. In this paper, a mathematical model for the HIV infection of \(CD4^+\) T cells is analyzed. We consider the proliferation of T cells in this study. It is found that there exist two equilibrium states for this model: Infection-free equilibrium state and infected equilibrium state. Local stability is discussed for both infection-free and infected equilibrium states using Routh--Hurwitz criteria. Also, we calculate the basic reproduction number \((R_0)\) for the model with the help of next generation matrix method. The global stability of the infection-free equilibrium point is discussed using Lyapunov's second method. From the stability analysis, it is found that if basic reproduction number \(R_0 \leq 1\), infection of HIV is cleared out, and if \(R_0 >1\), infection of HIV persists. The conditions for global stability of the infected equilibrium point are derived using a geometric approach. We find a parameter region where the infected equilibrium point is globally stable. We carry out numerical simulations to verify the results. Also, the effects of the proliferation rate of uninfected \(CD4^+\) T cells and recovery rate of infected \(CD4^+\) T cells in dynamics of the T cells and free virus are studied using numerical simulations. It is found that small variations of these parameters can change the model's whole dynamics, and infection can be controlled by controlling the proliferation rate and improving the recovery rate.
181
195
Bhagya Jyoti
Nath
Department of Mathematics
Barnagar College
India
bhagyajyotinath13@gmail.com
Kaushik
Dehingia
Department of Mathematics
Gauhati University
India
kaushikdehingia17@gmail.com
Hemanta Kumar
Sarmah
Department of Mathematics
Gauhati University
India
nsarmah@hotmail.com
HIV infection
global stability
\(CD4^+\) T cells
basic reproduction number
Article.2.pdf
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H. L. Smith, P. D. Leenheer, Virus dynamics: a global analysis, SIAM J. Appl. Math., 63 (2003), 1313-1327
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P. K. Srivastava, P. Chandra, Modeling the dynamics of HIV and $CD4^+$ T cells during primary infection, Nonlinear Anal. Real World Appl., 11 (2010), 612-618
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]
Co-prime order graphs of finite Abelian groups and dihedral groups
Co-prime order graphs of finite Abelian groups and dihedral groups
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en
The co-prime order graph \(\Theta (G)\) of a given finite group is a simple undirected graph whose vertex set is the group \(G\) itself, and any two vertexes \(x,y\) in \(\Theta (G)\) are adjacent if and only if \(gcd(o(x),o(y))=1\) or prime. In this paper, we derive a precise formula to count the vertex's degree in the co-prime order graph of a finite Abelian group or dihedral group.We also investigate the Laplacian spectrum of the co-prime order graph \(\Theta (G)\) when G is a finite Abelian p-group, \({\mathbb{Z}_p}^t \times {\mathbb{Z}_q}^s\) or a dihedral group \(D_{p^n}\).
196
202
Amit
Sehgal
Department of Mathematics
Pt. NRS Govt. College
India
amit_sehgal_iit@yahoo.com
Manjeet
Department of Mathematics
Pt. NRS Govt. College
India
sainimanjeet1994@gmail.com
Dalip
Singh
Department of Mathematics
Maharshi Dayanand University
India
dsmdur@gmail.com
Co-prime order graph
finite Abelian group
dihedral group
Laplacian spectrum
Article.3.pdf
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]
Hardy type inequalities for superquadratic functions via Jackson Nörlund integrals
Hardy type inequalities for superquadratic functions via Jackson Nörlund integrals
en
en
In this paper, it is tried to describe Hardy-type inequalities with certain kernels by using Jackson Nörlund integrals. In order to obtain the desired Hardy type inequalities, firstly, we prove Jensen's inequality involving super quadratic function and Jackson Nörlund integrals. Further, we discuss Hardy-type inequalities by choosing special kernels. Polya-Knopp type inequalities are also deduced to find applications.
203
212
Hafiz Abdul
Moeed
Department of Mathematics
University of Lahore
Pakistan
moeedmaths@gmail.com
Dawood
Ahmad
Department of Mathematics
University of Lahore
Pakistan
dawoodahmad.edu@gmail.com
Ammara
Nosheen
Department of Mathematics
University of Lahore
Pakistan
hammaran@gmail.com
Khuram Ali
Khan
Department of Mathematics
University of Sargodha
Pakistan
khuram.sms@gmail.com
Hahn integral operators
superquadratic function
Hardy-type inequalities
Article.4.pdf
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M. H. Annaby, A. E. Hamza, K. A. Aldwoah, Hahn difference operator and associated Jackson–Nörlund integrals, J. Optim. Theory Appl., 154 (2012), 133-153
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N. Ashraf, K. A. Khan, S. Mobeen, A. Nosheen, Inequalities of Hardy type for Jackson Nörlund Integrals, Commun. Math. Appli., 9 (2018), 411-419
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]
Error bounds associated with different versions of Hadamard inequalities of mid-point type
Error bounds associated with different versions of Hadamard inequalities of mid-point type
en
en
In this paper, we establish the error bounds of different versions of mid-point type inequalities.
At first, we prove two identities for fractional integrals involving the extended generalized
Mittag-Leffler function and generalized exponential fractional integrals, and then we establish the corresponding
error bound inequalities. Furthermore, we find a generalized inequality for error bound
inequalities using a generalized identity. Also, we find some inequalities which formulate all error
bound inequalities for various versions of Hadamard inequality. Finally, we present some examples of
the central moment of a random variable.
213
229
Muhammad
Raees
School of Natural Sciences
National University of Sciences and Technology
Pakistan
muhammad.raees@sns.nust.edu.pk
Matloob
Anwar
School of Natural Sciences
National University of Sciences and Technology
Pakistan
Ghulam
Farid
Department of Mathematics
COMSATS University Islamabad
Pakistan
Convex function
extended generalized Mittag-Leffler function
generalized integral
Hadamard inequality
Article.5.pdf
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N. S. Barnett, S. S. Dragomir, Some elementary inequalities for the expectation and variance of a random variable whose pdf is defined on a finite interval, Nova Sci. Publ., 2 (2002), 31-38
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H. Budak, F. Ertugral, M. Z. Sarikaya, New generalization of Hermite-Hadamard type inequalities via generalized fractional integrals, , (), -
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S. S. Dragomir, Inequalities of Jensen's type for generalized $k$-$g$-Fractional integrals of functions for which the composite $f\circ g^{-1}$ is convex, Fract. Differ. Calc., 8 (2018), 127-150
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G. Farid, Existence of an integral operator and its consequences in fractional calculus, Open J. Math. Sci., 3 (2019), 210-216
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G. Farid, M. Raees, M. Anwar, Bounds associated to Hadamard inequality via generalized integral operators and applications for conformable and fractional integrals, J. Fract. Calc. Appl., 11 (2020), 238-251
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A. Fernandez, P. O. Mohammed, Hermite-Hadamard inequalities in fractional calculus defined using Mittag-Leffler kernels, Math. Methods Appl. Sci., 2020 (2020), 1-18
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S. M. Kang, G. Farid, W. Nazeer, B. Tariq, Hadamard and Fejer–Hadamard inequalities for extended generalized fractional integrals involving special functions, J. Inequal. Appl., 2018 (2018), 1-11
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A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, Elsevier Science B.V., Amsterdam (2006)
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P. Kumar, Moments inequalities of a random variable defined over a finite interval, JIPAM. J. Inequal. Pure Appl. Math., 3 (2002), 1-11
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P. O. Mohammed, Hermite-Hadamard inequalities for Riemann-Liouville fractional integrals of a convex function with respect to a monotone function, Math. Meth. Appl. Sci., 2019 (2019), 1-11
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]
Presence and diversity of positive solutions for a Caputo-type fractional order nonlinear differential equation with an advanced argument
Presence and diversity of positive solutions for a Caputo-type fractional order nonlinear differential equation with an advanced argument
en
en
This article aims to construct the presence and diversity principles of minimum one or two positive solutions for a Caputo-type fractional-order nonlinear differential equation (CFONLDE for short) with an advanced argument under three-point boundary value conditions (BVCs for short). Guo-Krasnoselskii's fixed point theorem and Fixed-point index theory in cone spaces are used to analyze this article. First, the Green's function of the corresponding boundary value problem for a linear fractional differential equation with an advanced argument has been established. Next, several essential properties of that Green's function have been proved. Finally, in cone spaces, some novel presence and diversity principles of minimum of one or two positive solutions for a CFONLDE with an advanced argument are obtained. To support the analytic proof, some particular examples are included.
230
244
Md.
Asaduzzaman
Department of Mathematics
Islamic University
Bangladesh
masad_iu_math@yahoo.com
Adem
Kilicman
Department of Mathematics
Universiti Putra Malaysia
Malaysia
akilic@upm.edu.my
Md. Zulfikar
Ali
Department of Mathematics
University of Rajshahi
Bangladesh
alimath1964@gmail.com
CFONLDE with an advanced argument
three-point boundary value conditions
Guo-Krasnoselskii fixed point theorem
fixed-point index theory
positive solution
Article.6.pdf
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H. Afshari, M. Sajjadmanesh, D. Baleanu, Existence and uniqueness of positive solutions for a new class of coupled system via fractional derivatives, Adv. Differ. Equ., 2020 (2020), 1-18
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Y. Cu, W. Ma, Q. Sun, X. Su, New uniqueness results for boundary value problem of fractional differential equation, Nonlinear Anal. Model. Control, 23 (2018), 31-39
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F. H. Damag, A. Kilic¸man, A. T. Al-Arioi, On hybrid type nonlinear fractional integrodifferential equations, Mathematics, 8 (2020), 1-14
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A. Devi, A. Kumar, D. Baleanu, A. Khan, On stability analysis and existence of positive solutions for a general non-linear fractional differential equations, Adv. Differ. Equ., 2020 (2020), 1-16
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Global stability of delayed virus infection model including multi-target cells and B-cell impairment
Global stability of delayed virus infection model including multi-target cells and B-cell impairment
en
en
In this paper, we formulate a virus infection model with \(n\) classes of target
uninfected cells, \(n\) classes of latent infected cells, \(n\) classes of active infected cells, virus particles, and B cells. Three types of time delays and
the impairment of B cells are involved. The Well-posedness of the model is
demonstrated. Basic reproduction number of infection \(\mathcal{R}_{0}>0\) is
established, which determines the existence of equilibria as follows; when
\(\mathcal{R}_{0}\) is greater than unity, and then the model has two equilibria. Otherwise, the model has only a single equilibrium. The global stability of
equilibria is proven using Lyapunov's direct method and applying LaSalle's
invariance principle. To support our theoretical results, we have performed
some numerical simulations in case of \(n=2 \) where the model can describe the
HIV dynamics with two types of target cells, CD\(4^{+} \) T cells and macrophages.
245
262
Safiya F.
Alshehaiween
Department of Mathematics, Faculty of Science
Taibah University
Saudi Arabia
safiya.f.sh@gmail.com
Ahmed M.
Elaiw
Department of Mathematics, Faculty of Science
Department of Mathematics, Faculty of Science
King Abdulaziz University
Al-Azhar University
Saudi Arabia
Egypt
a_m_elaiw@yahoo.com
Virus dynamics
global stability
multi-target cells
impairment of B cells
time delay
Article.7.pdf
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]
Exact solutions of transaction cost nonlinear models for illiquid markets
Exact solutions of transaction cost nonlinear models for illiquid markets
en
en
The aim of this study is to show that the Reduced Differential Transform Algorithm (RDTA) can be applied to highly nonlinear evolution equations appearing in quantitative finance. In particular, we compute exact solutions of nonlinear PDEs arising by relaxing the transaction-cost assumption in the illiquid Black-Scholes market. Moreover, we also aim to study the impact of the absence and presence of price slippage impact in the illiquid Black-Scholes model with transaction-cost.
263
278
Javed
Hussain
Department of Mathematics
Sukkur IBA University
Pakistan
javed.brohi@iba-suk.edu.pk
Option pricing
relaxed Black-Scholes assumptions
evolution equation
differential transform
Article.8.pdf
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]