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2022
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Outbreak spatial pattern formation based on an SI model with the infected cross-diffusion term
Outbreak spatial pattern formation based on an SI model with the infected cross-diffusion term
en
en
This study is to discuss the pattern formations of a spatial epidemic model with cross-diffusion of the susceptible and infected groups simultaneously. The infected cross-diffusion term described the situation that the infected was allowed to move to areas with high density of the susceptible such as for work or study, especially after the pandemic. Turing analysis was applied to the model and yielded the conditions for Turing instability corresponding to the model. The amplitude equations were also given by the support of multiple-scale analysis, which then provided information about the stability of the patterns near the Turing bifurcation point. Numerical simulations revealed that there were five types of patterns, such as the spots, spots-stripes, stripes, stripes-holes, and holes. The holes indicated a disease outbreak in a region, while the spots showed non-outbreak. Furthermore, numerical simulations were carried out by varying the cross-diffusion coefficients of the susceptible and infected. The simulation results showed once the cross-diffusion coefficient of the infected was bigger than the susceptible, then an outbreak in a region was triggered. The results of this study showed that the movement of infected had a significant role in the spread of an infectious disease that could lead to another wave of pandemic. By using Turing analysis as a tool, as well as predator-prey model as the basis of movement theory, this paper tries to fill in the gaps in the discussion about the movement of infected people to areas with high density of the susceptible.
1
17
A.
Triska
Department of Mathematics, Faculty of Mathematics and Natural Sciences
Institut Teknologi Bandung
Indonesia
a.triska@s.itb.ac.id
A. Y.
Gunawan
Department of Mathematics, Faculty of Mathematics and Natural Sciences
Institut Teknologi Bandung
Indonesia
N.
Nuraini
Department of Mathematics, Faculty of Mathematics and Natural Sciences
Institut Teknologi Bandung
Indonesia
Cross-diffusion of the infected
spatial epidemic model
Turing pattern
Turing bifurcation
amplitude equations
Article.1.pdf
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]
Gronwall inequality and existence of solutions for differential equations with generalized Hattaf fractional derivative
Gronwall inequality and existence of solutions for differential equations with generalized Hattaf fractional derivative
en
en
The classical Gronwall inequality is one of the basic tools in the theory of differential and integral equations.
In this paper, a new version of this inequality is presented and extended to differential equations with the generalized Hattaf
fractional derivative involving non-singular kernel. The existence and uniqueness of solutions for such last type of
fractional differential equations are rigorously investigated. Furthermore, an application is presented to
study the Ulam-Hyers stability of certain equations.
18
27
Kh.
Hattaf
Equipe de Recherche en Modelisation et Enseignement des Mathematiques (ERMEM)
Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben Msik
Centre Regional des Metiers de l'Education et de la Formation (CRMEF)
Hassan II University of Casablanca
Morocco
Morocco
k.hattaf@yahoo.fr
A. A.
Mohsen
Department of Mathematics, College of Education for Pure Science (Ibn Al-Haitham)
Ministry of Education
University of Baghdad
Iraq
Iraq
H. F.
Al-Husseiny
Department of Mathematics, College of Education for Pure Science (Ibn Al-Haitham)
University of Baghdad
Iraq
Gronwall inequality
Hattaf fractional derivative
fractional differential equation
Ulam-Hyers stability
Article.2.pdf
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]
Optical solitons for conformable space-time fractional nonlinear model
Optical solitons for conformable space-time fractional nonlinear model
en
en
In search of the exact solutions of nonlinear partial differential
equations
in solitons form has become most popular to understand the internal features
of physical phenomena. In this paper, we discovered various type of solitons
solutions for the conformable space-time nonlinear Schrodinger equation (CSTNLSE)
with Kerr law nonlinearity. To seek such solutions, we applied two proposed methods
which are Sardar-subequation method and new extended hyperbolic function method.
In this way several types of solitons obtained for example bright, dark, periodic
singular, combined dark-bright, singular, and combined singular solitons.
Some of the acquired solutions are interpreted
graphically. These solutions are
specific, novel, correct and may be beneficial for edifying precise
nonlinear physical phenomena in nonlinear dynamical schemes. It is
revealed that the proposed methods offer a straightforward and
mathematical tool for solving nonlinear conformable space-time
nonlinear Schrodinger equation. These results support in attaining nonlinear optical fibers in the future.
28
41
M. I.
Asjad
Department of Mathematics
University of Management and Technology
Pakistan
imran.asjad@umt.edu.pk
N.
Ullah
Department of Mathematics
University of Management and Technology
Pakistan
H. u.
Rehman
Department of Mathematics
University of Okara
Pakistan
D.
Baleanu
Department of Mathematics
Institute of Space Sciences
Cankaya University
R76900 Magurele-Bucharest
Turkey
Romania
Sardar-subequation method
conformable space-time nonlinear Schrodinger equation
the new extended hyperbolic function method
optical solitons
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A. Sonomezoglu, S. Ortakaya, M. Eslami, A. Biswas, M. Mirzazadeh, M. Ekici, Solitons solutions to a few fractional nonlinear evolution equations in shallow water wave dynamics, Eur. Phys. J. Plus, 131 (2016), 166-177
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P. Suarez, A. Biswas, Exact 1-soliton solution of the Zakharov equation in plasmas with power law nonlinearity, Appl. Math. Comput., 217 (2011), 7372-7375
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Q. Zhou, S. P. Moshokoa, A. Biswas, M. Belic, M. Ekici, M. Mirzazadeh, Solitons in optical metamaterials with fractional temporal evolution, Optik, 127 (2016), 10879-10897
]
On solving variational inequality problems involving quasimonotone operators via modified Tseng's extragradient methods with convergence analysis
On solving variational inequality problems involving quasimonotone operators via modified Tseng's extragradient methods with convergence analysis
en
en
The main objective of this research is to find the numerical solution of variational inequalities involving quasimonotone operators in infinite-dimensional real Hilbert spaces. The main advantage of these iterative schemes is that they allow the uncomplicated calculation of step size rules that depend on the knowledge of an operator explanation instead of the Lipschitz constant or some other line search method. The proposed iterative schemes follow a monotone and non-monotone step size procedure based on mapping (operator) information as a replacement for its Lipschitz constant or some other line search method. The strong convergences are well proven, analogous to the proposed methods, and impose certain control specification conditions. Finally, to verify the effectiveness of the iterative methods, we present some numerical experiments.
42
58
N.
Wairojjana
Applied Mathematics Program, Faculty of Science and Technology
Valaya Alongkorn Rajabhat University under the Royal Patronage
Thailand
nopparat@vru.ac.th
N.
Pakkaranang
Mathematics and Computing Science Program, Faculty of Science and Technology
Phetchabun Rajabhat University
Thailand
nuttapol.pak@pcru.ac.th
S.
Noinakorn
Mathematics and Computing Science Program, Faculty of Science and Technology
Phetchabun Rajabhat University
Thailand
supansa.noi@pcru.ac.th
Variational inequality problem
Tseng's extragradient method
strong convergence theorems
quasimonotone operator
Lipschitz continuity
Article.4.pdf
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]
Solution of fractional autonomous ordinary differential equations
Solution of fractional autonomous ordinary differential equations
en
en
Autonomous differential equations of fractional order and non-singular kernel are solved. While solutions can be obtained through numerical, graphical, or analytical solutions, we seek an implicit analytical solution.
59
64
R.
AlAhmad
Mathematics department
Department of Mathematics and Natural Sciences
Yarmouk University
Higher colleges of technology
Jordan
UAE
rami_thenat@yu.edu.jo
Q.
AlAhmad
Mathematics Department
California state university at Northridge
USA
A.
Abdelhadi
Department of Mathematics and Natural Sciences
Higher colleges of technology
UAE
Fractional derivatives
Caputo fractional derivative
the Caputo-Fabrizio fractional derivative
Laplace transform
Article.5.pdf
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[1]
R. AlAhmad, Products of incomplete gamma functions, Analysis (Berlin), 36 (2016), 199-203
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R. AlAhmad, Products of Incomplete gamma functions Integral representations, Math. Sci. Appl. E-Notes, 4 (2016), 47-51
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H. R. Thieme, Mathematics in Population Biology, Princeton University Press, Princeton (2018)
]
Independent UP-algebras
Independent UP-algebras
en
en
In this paper, we introduce the concept of a new algebraic structure: independent UP-algebras (in short, IUP-algebras), which is independent of UP-algebras.
We also introduce the concepts of IUP-subalgebras, IUP-filters, IUP-ideals, and strong IUP-ideals of IUP-algebras and investigate their properties and relationships.
Finally, we discuss the concept of homomorphisms between IUP-algebras and also study the direct and inverse images of four special subsets.
65
76
A.
Iampan
Fuzzy Algebras and Decision-Making Problems Research Unit, Department of Mathematics, School of Science
University of Phayao
Thailand
aiyared.ia@up.ac.th
P.
Julatha
Department of Mathematics, Faculty of Science and Technology
Pibulsongkram Rajabhat University
Thailand
pongpun.j@psru.ac.th
P.
Khamrot
Faculty of Science and Agricultural Technology
Rajamangala University of Technology Lanna Phitsanulok
Thailand
pk_g@rmutl.ac.th
D. A.
Romano
International Mathematical Virtual Institute
Bosnia and Herzegovina
bato49@hotmail.com
UP-algebra
IUP-algebra
IUP-subalgebra
IUP-filter
IUP-ideal
strong IUP-ideal
Article.6.pdf
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[1]
M. A. Ansari, A. Haidar, A. N. A. Koam, On a graph associated to UP-algebras, Math. Comput. Appl., 23 (2018), 1-12
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P. Burandate, S. Thongarsa, A. Iampan, Fuzzy sets in UP-algebras with respect to a triangular norm, Konuralp J. Math., 7 (2019), 410-432
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N. Dokkhamdang, A. Kesorn, A. Iampan, Generalized fuzzy sets in UP-algebras, Ann. Fuzzy Math. Inform., 16 (2018), 171-190
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A. E. I. Elkabany, M. A. Abdel Naby, S. M. Mostafa, New view of ideals on PU-algebra, Int. J. Comput. Appl., 111 (2015), 9-15
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A. Iampan, Multipliers and near UP-filters of UP-algebras, J. Discrete Math. Sci. Cryptogr., 24 (2021), 667-680
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A. Iampan, M. Songsaeng, G. Muhiuddin, Fuzzy duplex UP-algebras, Eur. J. Pure Appl. Math., 13 (2020), 459-471
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K. Iseki, An algebra related with a propositional calculus, Proc. Japan Acad., 42 (1966), 26-29
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Y. B. Jun, G. Muhiuddin, D. A. Romano, On filters in UP-algebras, a review and some new reflections, J. Int. Math. Virtual Inst., 11 (2021), 35-52
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T. Klinseesook, S. Bukok, A. Iampan, Rough set theory applied to UP-algebras, J. Inform. Optim. Sci., 41 (2020), 705-722
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P. Mosrijai, A. Iampan, A new branch of bialgebraic structures: UP-bialgebras, J. Taibah Univ. Sci., 13 (2019), 450-459
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G. Muhiuddin, Bipolar fuzzy $KU$-subalgebras/ideals of $KU$-algebras, Ann. Fuzzy Math. Inform., 8 (2014), 409-418
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A. Rezaei, A. B. Saeid, K. Y. S. Saber, On pseudo-CI-algebras, Soft Comput., 23 (2019), 4643-4654
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A. Satirad, R. Chinram, A. Iampan, Four new concepts of extensions of KU/UP-algebras, Missouri J. Math. Sci., 32 (2020), 138-157
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A. Satirad, R. Chinram, A. Iampan, Pythagorean fuzzy sets in UP-algebras and approximations, AIMS Math., 6 (2021), 6002-6032
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A. Satirad, A. Iampan, Fuzzy soft sets over fully UP-semigroups, Eur. J. Pure Appl. Math., 12 (2019), 294-331
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A. Satirad, P. Mosrijai, A. Iampan, Formulas for finding UP-algebras, Int. J. Math. Comput. Sci., 14 (2019), 403-409
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A. Satirad, P. Mosrijai, A. Iampan, Generalized power UP-algebras, Int. J. Math. Comput. Sci., 14 (2019), 17-25
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T. Senapati, G. Muhiuddin, K. P. Shum, Representation of UP-algebras in interval-valued intuitionistic fuzzy environment, Ital. J. Pure Appl. Math., 38 (2017), 497-517
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J. Somjanta, N. Thuekaew, P. Kumpeangkeaw, A. Iampan, Fuzzy sets in UP-algebras, Ann. Fuzzy Math. Inform., 12 (2016), 739-756
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S. Thongarsa, P. Burandate, A. Iampan, Some operations of fuzzy sets in UP-algebras with respect to a triangular norm, Ann. Commun. Math., 2 (2019), 1-10
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P. Yiarayong, P. Wachirawongsakorn, A new generalization of BE-algebras, Heliyon, 4 (2018), 1-11
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]
Maximal elements for Kakutani maps
Maximal elements for Kakutani maps
en
en
We present some new general existence theorems for maximal type elements for upper semicontinuous maps with convex compact values.
77
85
D.
O'Regan
School of Mathematical and Statistical Sciences
National University of Ireland
Ireland
donal.oregan@nuigalway.ie
Fixed and coincidence point theory
maximal elements
Article.7.pdf
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R. P. Agarwal, D. O'Regan, S. Park, Fixed point theory for multimaps in extension type spaces, J. Korean Math. Soc., 39 (2002), 579-591
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D. O'Regan, Deterministic and random fixed points for maps on extension type spaces, Appl. Anal., 97 (2018), 1960-1966
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D. O'Regan, Collectively coincidence type results and applications, Appl. Anal., 2021 (2021), 1-12
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D. O'Regan, A note on collectively fixed and coincidence points, to appear, ()
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K.-K. Tan, X.-Z. Yuan, Maximal elements and equilibria for ${\cal U}$--majorised preferences, Bull. Austral. Math. Soc., 49 (1994), 47-54
]
Some fixed point results in partially ordered E metric space
Some fixed point results in partially ordered E metric space
en
en
The existence and uniqueness of the fixed point theorem for self mapping
meeting certain contractive conditions in partially ordered \(E\) metric
spaces with non-normal positive cone \(E^{+}\) of a real normed space \(E\) with
empty interior are investigated in this research.
86
96
A.
Nuseir
Mathematics Department
JUST University
Jordan
Sh.
Al-Sharif
Mathematics Department
Yarmouk University
Jordan
sharifa@yu.edu.jo
Fixed point
positive cone
normed space
Article.8.pdf
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