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2021
14
4
ISSN 2008-1898
105
Results on solvability of nonlinear quadratic integral equations of fractional orders in Banach algebra
Results on solvability of nonlinear quadratic integral equations of fractional orders in Banach algebra
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en
Here, we investigate the existence result for a nonlinear quadratic functional integral equation of fractional order using a fixed point theorem of Dhage. The continuous dependence of solution on the delay functions will be studied. As an application, an existence theorem for the fractional hybrid differential equations is proved. Also, we study a general quadratic integral equation of fractional order.
181
195
Sh. M.
Al-Issa
Department of Mathematics, faculty of Art and Science
Department of Mathematics, faculty of Art and Science
Lebanese International University
Lebanese International University
Lebanon
Lebanon
shorouk.alissa@liu.edu.lb
N. M.
Mawed
Department of Mathematics, faculty of Art and Science
Lebanese International University
Lebanon
31430473@students.liu.edu.lb
Dhage fixed point theorem
continuous dependence of solutions
hybrid differential equations
general quadratic integral equation
Article.1.pdf
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[1]
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B. C. Dhage, A fixed point theorem in Banach algebras involving three operators with applications, Kyungpook Math. J., 44 (2004), 145-155
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]
SIQR dynamics in a random network with heterogeneous connections with infection age
SIQR dynamics in a random network with heterogeneous connections with infection age
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In this paper, an SIQR-Epidemic transmission model of the non-Markovian infection process and quarantine process in a heterogeneous complex network is established, in which the infection rate and quarantine rate are related to infection age. Next, we use the method of characteristics to transform the model into an integro-differential equation and derive the epidemic threshold of the model. Finally, we focus on the impact of three different infection or quarantine time distributions on the disease transmission and show that infection or quarantine time distribution has a significant effect on the disease dynamics.
196
211
Hairong
Yan
School of Mathematical Sciences
Shanxi University
P.R. China
864415225@qq.com
Jinxian
Li
School of Mathematical Sciences
Shanxi University
P.R. China
ljxsmile1@163.com
SIQR-epidemic
complex network
infection age
non-Markovian transmission and quarantine
epidemic threshold
Article.2.pdf
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S. Chen, M. Small, Y. Tao, X. Fu, Transmission Dynamics of an SIS Model with Age Structure on Heterogeneous Networks, Bull. Math. Biol., 80 (2018), 2049-2087
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S. He, Y. Peng, K. Sun, SEIR modeling of the COVID-19 and its dynamics, Nonlinear Dyn., 101 (2020), 1667-1680
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G. Herzog, R. Redheffer, Nonautonomous SEIRS and Thron models for epidemiology and cell biology, Nonlinear Anal. Real World Appl., 5 (2004), 33-44
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W. Jing, Z. Jin, J. Zhang, An SIR pairwise epidemic model with infection age and demography, J. Biol. Dyn., 12 (2018), 486-508
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Q. Liu, H. Li, Global dynamics analysis of an SEIR epidemic model with discrete delay on complex network, Phys. A, 524 (2019), 289-296
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]
\(a\)-minimal prime ideals in almost distributive lattices
\(a\)-minimal prime ideals in almost distributive lattices
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The concept of \(a\)-minimal prime ideal of an ADL is introduced and its characterizations are established. The set of all \(a\)-minimal prime ideals of an ADL is topologized and resulting space is studied.
212
221
Ch. Santhi Sundar
Raj
Department of Engineering Mathematics
Andhra University
India
santhisundarraj@yahoo.com
K. Ramanuja
Rao
Deaprtment of Mathematics
Fiji National Uniersity
FIJI
ramanuja.kotti@fnu.ac.fj
S. Nageswara
Rao
Department of Engineering Mathematics
Andhra University
India
bollasubrahmanyam@gamil.com
ADL
minimal prime ideal
relative
\(a\)-annihilator
\(a\)-minimal prime ideal
\(a\)-maximal filter
\(a\)-pseudo complementation
hull-kernel topology
Article.3.pdf
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M. Mandelker, Relative annhilators in lattices, Duke Math. J., 37 (1970), 377-386
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C. S. Sundar Raj, S. N. Rao, K. R. Rao, $\mathtt{a}$-pseudo complementation on an ADL's, Asian-Eur. J. Math., 2020 (2020), -
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]
Generalized Kantorovich-Szász type operations involving Charlier polynomials
Generalized Kantorovich-Szász type operations involving Charlier polynomials
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en
The purpose of this paper is to introduce a new kind of Kantorovich-Szász type operators based on Charlier polynomials and study its various approximation properties. We establish some local direct theorems, e.g., Voronovskaja type asymptotic theorem and an estimate of error by means of the Lipschitz type maximal function and the Peetre's K-functional. We also discuss the weighted approximation properties. Next, we construct a bivariate case of the above operators and study the degree of approximation with the aid of the complete and partial moduli of continuity. A Voronovskaja type asymptotic theorem and the order of convergence by considering the second order modulus of continuity are also proved. We define the associated Generalized Boolean Sum (GBS) operators and discuss the degree of approximation by using mixed modulus of smoothness for Bögel continuous and Bögel differentiable functions. Furthermore, by means of a numerical example it is shown that the proposed operators provide us a better approximation than the operators corresponding to the particular case \(\wp=1\). We also illustrate the convergence of the bivariate operators and the associated GBS operators to a certain function and show that the GBS operators enable us a better error estimation than the bivariate operators using Matlab algorithm.
222
249
P. N.
Agrawal
Department of Mathematics
Indian Institute of Technology Roorkee
India
pnappfma@gmail.com
Abhishek
Kumar
Department of Mathematics
Indian Institute of Technology Roorkee
India
anikk6887@gmail.com
Aditi Kar
Gangopadhyay
Department of Mathematics
Indian Institute of Technology Roorkee
India
aditifma@iitr.ac.in
Tarul
Garg
Department of Applied Science
The NorthCap University
India
tarulgarg@ncuindia.edu
Voronovskaya theorem
moduli of continuity
Peetre's K-functional
Bögel continuous function
Bögel differentiable function
Article.4.pdf
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P. N. Agrawal, N. Ispir, Degree of approximation for bivariate Chlodowsky-Szasz-Charlier type operators, Results. Math., 69 (2016), 369-385
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D. Barbosu, C. V. Muraru, Approximating B-continuous functions using GBS operators of Bernstein-Schurer-Stancu type based on q-integers, Appl. Math. Comput., 259 (2015), 80-87
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K. Bogel, Über mehrdimensionale Differentiation, Integration und beschränkte Variation, J. Reine Angew. Math., 173 (1935), 5-30
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M. A. Ozarslan, O. Duman, Smoothness properties of modified Bernstein-Kantorovich operators, Numer. Funct. Anal. Optim., 37 (2016), 92-105
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J. Peetre, Theory of Interpolation of Normal Spaces, Lecture Notes, Brasilia (1963)
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O. Szasz, Generalization of S. Bernstein’s polynomials to be infinite interval, J. Res. Natl. Bur. Stand., 45 (1952), 239-245
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]
The Marshall-Olkin-Gompertz-G family of distributions: properties and applications
The Marshall-Olkin-Gompertz-G family of distributions: properties and applications
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en
We develop a new generalized family of the Gompertz-G distribution, namely, the Marshall-Olkin-Gompertz-G distribution. Statistical properties of the new proposed model are presented. Some special cases of the new family of distributions are presented. Maximum likelihood estimates of the model parameters are also determined. A simulation study was conducted to assess the performance of the maximum likelihood estimates. Applications to demonstrate the usefulness of the Marshall-Olkin-Gompertz-Weibull distribution to real data examples are provided.
250
267
Fastel
Chipepa
Department of Mathematical Statistics
Department of Applied Mathematics and Statistics
Botswana International University of Science and Technology
Midlands State University
Botswana
Zimbabwe
chipepaf@staff.msu.ac.zw
Broderick
Oluyede
Department of Mathematical Statistics
Botswana International University of Science and Technology
Botswana
oluyedeo@biust.ac.bw
Gompertz-G distribution
Marshall-Olkin-G distribution
maximum likelihood estimation
Article.5.pdf
[
]
The odd Weibull-Topp-Leone-G power series family of distributions: model, properties, and applications
The odd Weibull-Topp-Leone-G power series family of distributions: model, properties, and applications
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en
A new generalization of the odd Weibull-Topp-Leone-G family of distributions called the odd Weibull-Topp-Leone-G power series family of distributions is developed. Statistical properties of the new distribution were derived. We also derive the maximum likelihood estimates of the proposed model. Some special cases for the new family of distributions were also considered. We conducted a simulation study to evaluate the consistency of the maximum likelihood estimates. Two real data examples were also considered to demonstrate the usefulness of the newly proposed family of distributions.
268
286
Broderick Oluyede
Department of Mathematical Statistics
Botswana International University of Science and Technology
Botswana
oluyedeo@biust.ac.bw
Fastel
Chipepa
Department of Mathematical Statistics
Department of Applied Mathematics and Statistics
Botswana International University of Science and Technology
Midlands State University
Botswana
Zimbabwe
chipepaf@staff.msu.ac.zw
Divine
Wanduku
Department of Mathematical Sciences
Georgia Southern University
USA
dwanduku@georgiasouthern.edu
Odd Weibull-Topp-Leone-G
odd Weibull-G
Topp-Leone-G distribution
power series distribution
Article.6.pdf
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