]>
2020
20
2
109
On dynamics of fractional-order oncolytic virotherapy models
On dynamics of fractional-order oncolytic virotherapy models
en
en
In this paper, we provide a mathematical model with a fractional-order to investigate the dynamics of oncolytic virotherapy. We focus on how the dynamics of oncolytic virotherapy models can rely on the burst size of the virus. The burst size of a virus is the number of new viruses released from the lysis of an infected cell. Different viruses have different burst sizes. The numerical simulations confirm that the fractional-order differential models have the ability can provide accurate descriptions of oncolytic virotherapy models and capture the memory of the dynamics.
79
87
Abdullah
Abu-Rqayiq
Department of Mathematics and Statistics
Texas A \& M University-Corpus Christi
USA
abdullah.aburqayiq@tamucc.edu
Mohammad
Zannon
Department of Mathematics and Statistics
Tafilah Technical University
Jordan
Fractional calculus
oncolytic virotherapy
immune innate response
equilibrium points
local stability
Article.1.pdf
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I. Podlubny, Fractional Differential Equations, Academic Press, San Diego (1999)
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J. A. Tenreiro Machado, Entropy analysis of integer and fractional dynamical systems, Nonlinear Dynam., 62 (2010), 371-378
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J. P. Tian, The replicability of oncolytic virus: defining conditions in tumor virotherapy, Math. Biosci. Eng., 8 (2011), 841-860
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L. M. Wein, J. T. Wu, D. H. Kirn, Validation and analysis of a mathematical model of a replication-competent oncolytic virus for cancer treatment: Implications for virus design and delivery, Cancer Research, 63 (2003), 1317-1324
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D. Wodarz, Viruses as antitumor weapons: defining conditions for tumor remission, Cancer Research, 61 (2001), 3501-3507
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D. Wodarz, Computational approaches to study oncolytic virutherapy: insights and challenges, Gene. Ther. Mol. Biol., 8 (2004), 137-146
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J. T. Wu, H. M. Byrne, D. H. Kirn, L. M. Wein, Modeling and analysis of a virus that replicates selectively in tumor cells, Bull. Math. Biol., 63 (2001), 731-768
]
A Qi formula for translated \(r\)-Dowling numbers
A Qi formula for translated \(r\)-Dowling numbers
en
en
Another form of an explicit formula for translated \(r\)-Dowling numbers is derived using Faa di Bruno's formula and certain identity of Bell polynomials of the second kind. This formula is expressed in terms of the translated \(r\)-Whitney numbers of the second kind and the ordinary Lah numbers, which is analogous to Qi formula. As a consequence, a relation between translated \(r\)-Dowling numbers and the sums of row entries of the product of two matrices containing the translated \(r\)-Whitney numbers of the second kind and the ordinary Lah numbers is established.
88
100
Roberto B.
Corcino
Research Institute for Computational Mathematics and Physics
Cebu Normal University
Philippines
rcorcino@yahoo.com
Cristina B.
Corcino
Research Institute for Computational Mathematics and Physics
Cebu Normal University
Philippines
cristinacorcino@yahoo.com
Jeneveb T.
Malusay
Research Institute for Computational Mathematics and Physics
Cebu Normal University
Philippines
ferdie_malusay@yahoo.com
Qi formula
Translated \(r\)-Dowling numbers
Bell polynomials
Lah numbers
translated \(r\)-Whitney numbers
Faa di Bruno's formula
\(r\)-Whitney-Lah numbers
Article.2.pdf
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I. Area, E. Godoy, A. Ronveaux, A. Zarzo, Classical Discrete Orthogonal Polynomials, Lah Numbers, and Involutory Matrices, Appl. Math. Lett., 16 (2003), 383-387
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H. Belbachir, I. E. Bousbaa, Translated Whitney and $r$-Whitney Numbers: A Combinatorial Approach, J. Integer Seq., 16 (2013), 1-7
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M. Benoumhani, On Whitney Numbers of Dowling Lattices, Discrete Math., 159 (1996), 13-33
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K. N. Boyadzhiev, Lah Numbers, Laguerre Polynomials of Order Negative One, and the $n$th Derivative of $\exp(1/x)$, Acta Univ. Sapientiae Math., 8 (2016), 22-31
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G.-S. Cheon, J.-H. Jung, $r$-Whitney numbers of Dowling Lattices, Discrete Math., 312 (2012), 2337-2348
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S. Daboul, J. Mangaldan, M. Z. Spivey, P. J. Taylor, The Lah Numbers and the $n$th Derivative of $e^\frac{1}{x}$, Math. Mag., 86 (2013), 39-47
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B.-N. Guo, F. Qi, Six Proofs for an Identity of the Lah Numbers, Online J. Anal. Comb., 10 (2015), 1-5
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E. Gyimesi, G. Nyul, New combinatorial interpretations of $r$-Whitney and r-Whitney-Lah numbers, Discrete Appl. Math., 255 (2019), 222-233
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I. Mező, On the Maximum of $r$-Stirling numbers, Adv. in Appl. Math., 41 (2008), 293-306
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I. Mező, The $r$-Bell Numbers, J. Integer Seq., 14 (2011), 1-14
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F. Qi, An Explicit Formula for the Bell Numbers in terms of Lah and Stirling Numbers, Mediterr. J. Math., 13 (2016), 2795-2800
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X.-J. Zhang, F. Qi, W.-H. Li, Properties of three functions relating to the exponential function and the existence of partitions of unity, Int. J. Open Probl. Comput. Sci. Math., 5 (2012), 122-127
]
Application of Shehu transform to Atangana-Baleanu derivatives
Application of Shehu transform to Atangana-Baleanu derivatives
en
en
Recently, Shehu Maitama and Weidong Zhao proposed a new integral transform,
namely, Shehu transform, which generalizes both the Sumudu and Laplace integral transforms. In this paper, we present new further properties of this transform. We apply this transformation to Atangana--Baleanu derivatives in Caputo and in Riemann--Liouville senses to solve some fractional differential equations.
101
107
Ahmed
Bokhari
Department of Mathematics, Faculty of Exact Sciences and Informatics
Hassiba Benbouali University of Chlef
Algeria
bokhari.ahmed@ymail.com
Dumitru
Baleanu
Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences
Institute of Space Science
Cankaya University
Turkey
Romania
dumitru.baleanu@gmail.com
Rachid
Belgacem
Department of Mathematics, Faculty of Exact Sciences and Informatics
Hassiba Benbouali University of Chlef
Algeria
belgacemrachid02@yahoo.fr
Shehu transform
Mittag-Leffler kernel
non-singular and non-local fractional operators
Article.3.pdf
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[1]
A. Atangana, R. T. Alqahtani, Numerical approximation of the space-time Caputo-Fabrizio fractional derivative and application to groundwater pollution equation, Adv. Difference Equ., 2016 (2016), 1-13
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A. Atangana, D. Baleanu, New Fractional Derivatives with Nonlocal and Non-Singular Kernel: Theory and Application to Heat Transfer Model, Thermal Sci., 20 (2016), 763-769
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A. Atangana, A. Kılıçman, The use of Sumudu transform for solving certain nonlinear fractional heat-like equations, Abstr. Appl. Anal., 2013 (2013), 1-12
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A. Atanganaa, I. Koca, Chaos in a simple nonlinear system with Atangana-Baleanu derivatives with fractional order, Chaos Solitons Fractals, 89 (2016), 447-454
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H. Bulut, H. M. Baskonus, F. B. M. Belgacem, The Analytical Solution of Some Fractional Ordinary Differential Equations by the Sumudu Transform Method, Abstr. Appl. Anal., 2013 (2013), 1-6
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Q. D. Katatbeh, F. B. M. Belgacem, Applications of the Sumudu transform to fractional differential equations, Nonlinear Stud., 18 (2011), 99-112
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S. Maitama, W. Zhao, New Integral Transform: Shehu Transform a Generalization of Sumudu and Laplace Transform for Solving Differential Equations, Int. J. Anal. Appl., 17 (2019), 167-190
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G. Mittag-Leffler, Sur la Nouvelle Fonction $E_{\alpha}(x)$, Comptes Rendus de l'Academie des Sciences Paris, 137 (1903), 554-558
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N. A. Shah, I. Khan, Heat transfer analysis in a second grade fluid over and oscillating vertical plate using fractional Caputo-Fabrizio derivatives, Eur. Phys. J. C, 76 (2016), 1-11
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D. Zhaoa, M. Luo, Representations of acting processes and memory effects: General fractional derivative and its application to theory of heat conduction with finite wave speeds, Appl. Math. Comput., 346 (2019), 531-544
]
Approximate controllability of semilinear strongly damped wave equation with impulses, delays, and nonlocal conditions
Approximate controllability of semilinear strongly damped wave equation with impulses, delays, and nonlocal conditions
en
en
In this paper, we prove that the interior approximate controllability of the linear strongly damped wave equation is not destroyed if we add impulses, nonlocal conditions, and a nonlinear perturbation with delay in the state. Specifically, we prove the interior approximate controllability of the semilinear strongly damped wave equation with impulses, delays, and nonlocal conditions. This is done by applying Roth's Fixed Point Theorem and the compactness of the semigroup generated by the linear uncontrolled system. Finally, we present some open problems and a possible general framework to study the controllability of impulsive semilinear second-order diffusion process in Hilbert spaces with delays and nonlocal conditions.
108
121
Cosme
Duque
Departamento de Matematicas
Universidad de Los Andes
Venezuela
duquec@ula.ve
Jahnett
Uzcategui
Departamento de Matematicas
Universidad de Los Andes
Venezuela
jahnettu@ula.ve
Hugo
Leiva
School of Mathematical and Computational Sciences
University YachayTech
Ecuador
hleiva@yachaytech.edu.ec
Oscar
Camacho
Departamento de Automatizacion y Control Industrial
Escuela Politecnica Nacional
Ecuador
oscar.camacho@epn.edu.ec
Interior approximate controllability
impulsive semilinear strongly damped wave equation with delays and nonlocal conditions
strongly continuous semigroups
Rothe's fixed point theorem
Article.4.pdf
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P. G. Wang, C. R. Li, J. Zhang, T. X. Li, Quasilinearization Method for First-Order Impulsive Integro-Differential Equations, Electron. J. Differential Equations, 2019 (2019), 1-14
]
Fractional calculus formulas for Mathieu-type series and generalized Mittag-Leffler function
Fractional calculus formulas for Mathieu-type series and generalized Mittag-Leffler function
en
en
Fractional calculus is allowing integrals and derivatives of any positive order (the term `fractional' kept only for historical reasons), which can be considered a branch of mathematical physics which mainly deals with integro-differential equations, where integrals are of convolution form with weakly singular kernels of power-law type. In recent decades fractional calculus has won more and more interest in applications in several fields of applied sciences. In this line, our main object to investigate image formulas of generalized fractional hypergeometric operators involving the product of Mathieu-type series and generalized Mittag-Leffler function. We also consider some interesting special cases of derived results by specializing suitable value of the parameters.
122
130
Owais
Khan
Department of Applied Mathematics
Aligarh Muslim University
India
owkhan05@gmail.com
Serkan
Araci
Department of Economics, Faculty of Economics, Administrative and Social Sciences
Hasan Kalyoncu University
Turkey
mtsrkn@hotmail.com
Mohd
Saif
Department of Applied Mathematics
Aligarh Muslim University
India
usmanisaif153@gmail.com
Fractional calculus operators
Mathieu-type series
generalized Mittag-Leffler function
Fox-Wright function
Article.5.pdf
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[1]
P. Agarwal, J. J. Nieto, Some fractional integral formulas for the Mittag-Leffler type function with four parameters, Open Math., 13 (2015), 537-546
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M. Arshad, J. S. Choi, S. Mubeen, K. S. Nisar, G. Rahman, A new extension of the Mittag-Leffler function, Commun. Korean Math. Soc., 33 (2018), 549-560
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M. Kamarujjama, O. Khan, Computation of new class of integrals involving generalized Galue type Struve function, J. Comput. Appl. Math., 351 (2019), 228-236
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M. Kamarujjama, N. U. Khan, O. Khan, The generalized $p$-$k$-Mittag-Leffler function and solution of fractional kinetic equation, J. Anal., 2019 (2019), 1-18
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M. Kamarujjama, N. U. Khan, O. Khan, J. J. Nieto, Extended type $k$-Mittag-Leffler function and its applications, Int. J. Appl. Comput. Math., 4 (2019), 1-14
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Some operations on hesitant fuzzy soft sets over UP-algebras
Some operations on hesitant fuzzy soft sets over UP-algebras
en
en
This paper aim is to apply the notions of the (restricted) union, the (extended) intersection, the \(\mathrm{AND}\), and the \(\mathrm{OR}\) of any hesitant fuzzy soft set to UP-algebras.
Moreover, we discuss results of the intersection and the union of hesitant fuzzy sets on UP-algebras and also apply the notions of the hesitant union and the hesitant intersection of hesitant fuzzy sets to UP-algebras.
131
154
Phakawat
Mosrijai
Department of Mathematics, School of Science
University of Phayao
Thailand
phakawat.mo@gmail.com
Aiyared
Iampan
Department of Mathematics, School of Science
University of Phayao
Thailand
aiyared.ia@up.ac.th
UP-algebra
hesitant fuzzy soft set
anti-hesitant fuzzy soft set
hesitant union
hesitant intersection
Article.6.pdf
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Semi-analytical solution for a system of competition with production a toxin in a chemostat
Semi-analytical solution for a system of competition with production a toxin in a chemostat
en
en
The resolution of a system for modeling the competition between opponents in a chemostat when one of these can produce a toxin has been studied. We propose a novel method to overcome the analytical difficulties of standard mathematical methods. The method is based on the variational iteration method and combined with the Gauss-Seidel technique for increasing the convergence rate. Numerical examples are considered to demonstrate the practicality and improve the convergence of the proposed method.
155
160
Aisha Abdullah
Alderremy
Mathematics Department, College of Sciences
King Khalid University
KSA
aaldramy@kku.edu.sa
Mourad
Chamekh
Mathematics Department, College of Sciences and Arts, AlKamel
National Engineering School at Tunis
University of Jeddah
University of Tunis El Manar
KSA
Tunisia
mourad.chamekh@enit.utm.tn
Fadhel
Jeday
Mathematics Department, Jamoum College
National Engineering School at Tunis
Umm Al-Qura University
University of Tunis El Manar
KSA
Tunisia
fadheldj@yahoo.com
VIM
semi-analytical solution
nonlinear Gauss-Seidel method
opponents in a chemostat
Article.7.pdf
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Global dynamics of delayed HIV infection models including impairment of B-cell functions
Global dynamics of delayed HIV infection models including impairment of B-cell functions
en
en
In this paper, we construct delayed HIV dynamics models with impairment of B-cell functions. Two forms of the incidence rate have been considered,
bilinear and general. Three types of infected cells and five-time delays have been incorporated into the models. The well-posedness of the models is justified. The models admit two equilibria, which are determined by the basic reproduction number \(R_{0}\). The global stability of each equilibrium is proven by utilizing the Lyapunov function and LaSalle's invariance principle.
Numerical simulations illustrate the theoretical results.
161
188
Ahmed
Elaiw
Department of Mathematics, Faculty of Science
King Abdulaziz University
Saudi Arabia
a_m_elaiw@yahoo.com
Safiya
Alshehaiween
Department of Mathematics, Faculty of Science
Department of Mathematics, Faculty of Science
King Abdulaziz University
Taibah University
Saudi Arabia
Saudi Arabia
safiya.f.sh@gmail.com
Aatef
Hobiny
Department of Mathematics, Faculty of Science
King Abdulaziz University
Saudi Arabia
ahobany@kau.edu.sa
HIV dynamics
global stability
Lyapunov function
B-cell impairment
latent reservoirs
time delay
Article.8.pdf
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]