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Connectedness, local connectedness, and components on bipolar soft generalized topological spaces
Connectedness, local connectedness, and components on bipolar soft generalized topological spaces
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Connectedness represents the most significant and fundamental topological property. It highlights the main characteristics of topological spaces and distinguishes one topology from another. There is a constant study of bipolar soft generalized topological spaces (\( \mathcal{BSGTS}s \)) by presenting \(\mathcal{BS}\) \( \widetilde{\widetilde{\mathfrak{g}}} \)-connected set and \(\mathcal{BS}\) \( \widetilde{\widetilde{\mathfrak{g}}} \)-connected space in \(\mathcal{BSGTS}s\) as well as it is discussing some properties and results for these topics. Additionally, the notion of bipolar soft disjoint sets is put forward, \(\mathcal{BS} \) \(\widetilde{\widetilde{\mathfrak{g}}}\)-separation set, \(\widetilde{\widetilde{\mathfrak{g}}}\)-separated \(\mathcal{BSS}s\) and \(\mathcal{BS}\) \( \widetilde{\widetilde{\mathfrak{g}}} \)-hereditary property. Moreover, there is an extensive study of \(\mathcal{BS}\) \( \widetilde{\widetilde{\mathfrak{g}}} \)-locally connected space and \(\mathcal{BS}\) \( \widetilde{\widetilde{\mathfrak{g}}} \)-component with some related properties and theorems following them, such as the concepts of \( \mathcal{BS} \) \(\widetilde{\widetilde{\mathfrak{g}}}\)-locally connected spaces and \( \mathcal{BS} \) \(\widetilde{\widetilde{\mathfrak{g}}}\)-connected are independent of each other; also determined the conditions under which the \( \mathcal{BS} \) \(\widetilde{\widetilde{\mathfrak{g}}}\)-connected subsets are \( \mathcal{BS} \) \(\widetilde{\widetilde{\mathfrak{g}}}\)-components.
302
321
H. Y.
Saleh
Department of Mathematics, College of Basic Education
University of Duhok
Iraq
B. A.
Asaad
Department of Computer Science, College of Science
Department of Mathematics, Faculty of Science
Cihan University
University of Zakho
Iraq
Iraq
baravan.asaad@uoz.edu.krd
R. A.
Mohammed
Department of Mathematics, College of Basic Education
University of Duhok
Iraq
\(\mathcal{BSGTS}\)
\( \widetilde{\widetilde{\mathfrak{g}}}\)-separated \(\mathcal{BSS}s\)
\(\mathcal{BS}\) \( \widetilde{\widetilde{\mathfrak{g}}}\)-connected set
\( \mathcal{BS}\) \( \widetilde{\widetilde{\mathfrak{g}}} \)-connected space
\(\mathcal{BS}\) \( \widetilde{\widetilde{\mathfrak{g}}}\)-locally connected space
\(\mathcal{BS}\) \( \widetilde{\widetilde{\mathfrak{g}}}\)-component
Article.1.pdf
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On the existence and stability of Caputo Volterra-Fredholm systems
On the existence and stability of Caputo Volterra-Fredholm systems
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In this paper, we discuss several problems related to the neutral fractional Volterra-Fredholm integro-differential systems in Banach spaces. Existence of the
Schaefer's fixed point and Ulam-Hyers-Rassias stability properties for the fixed point problem will be discussed. Some results are presented, under appropriate conditions, and
some open questions are pointed out. Our results extend recent results given for \(\psi\)-fractional derivative.
322
331
S. A. M.
Jameel
Department of Computer Systems
Middle Technical University, Institute of Administration Rusafa
Iraq
saif\_aldeen2001@mtu.edu.iq
\(\psi\)-Caputo fractional derivative
integro-differential equation
fixed point technique
stability problem
Article.2.pdf
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Generalized neutrosophic ideal convergent sequence spaces
Generalized neutrosophic ideal convergent sequence spaces
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Kostyrko et al. initiated the concept of ideal convergence in [P. Kostyrko, T. Šalát, W. Wilczyński, Real Anal. Exchange, \(\bf 26\) (2000), 669--686]. The purpose of this paper is to introduce and define spaces of the neutrosophic convergent sequence via ideal, namely \(^{I}\mathcal{S}_{\mathcal{M}}\) and \(^{I}\mathcal{S}_{\mathcal{M}_{0}}\). We prove that new spaces are linear and Hausdorff topological spaces. Further, we examine the relation between \(I\)-Cauchy and \(I\)-convergent sequences and show that every separable space \(^{I}\mathcal{S}_{\mathcal{M}}\) is second countable. Moreover, we prove that the space \(^{I}\mathcal{S}_{\mathcal{M}}\) is complete.
332
339
M.
Ahmad
Department of Mathematics
Presidency University, School of Engineering
India
mobeenahmad88@gmail.com
M. I.
Idrisi
Department of Mathematics
University Institute of Sciences, Chandigarh University
India
A. K.
Sirohi
School of Computational and Integrative Sciences
Jawaharlal Nehru University
India
Ideal
filter
\(I\)-convergence
\(I\)-Cauchy
\(t\)-norm
\(t\)-conorm
neutrosophic normed space
Article.3.pdf
[
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Theoretical study and numerical simulation for a mathematical model of diffusive cancer with effect of stem cell therapy and chemotherapy
Theoretical study and numerical simulation for a mathematical model of diffusive cancer with effect of stem cell therapy and chemotherapy
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Cancer is the most dangerous disease in the world. Therefore, this paper is devoted to studying a mathematical model of diffusive cancer and the effect of its treatments. One of the cancer treatments currently being explored is stem cell transplant, which works to stimulate and strengthen the immune system while the patient receives chemotherapy.
This work introduces a mathematical system for the temporal and spatial interactions between the tumor, stem cells and effector cells during chemotherapy and the extent of the spread of these interactions within the tissue. Also, we study the stability of the system through the equilibrium points of the reaction-diffusion model. In addition, the existence, uniqueness, positivity, and boundedness are proven. We found a numerical simulation by the finite difference method and observed a dynamic of the solutions. Also, we described the tumor behaviour before and after the treatments and the effect of its diffusion.
340
351
N. H.
Aljahdaly
Department of Mathematics, Faculty of Sciences and Arts
King Abdulaziz University
Saudi Arabia
Nhaljahdaly@kau.edu.sa
N. A.
Almushaity
Department of Mathematics, Faculty of Sciences and Arts
King Abdulaziz University
Saudi Arabia
Cancer mathematical model
chemotherapy therapy
stem cell transplant
diffusion terms
finite difference method
Article.4.pdf
[
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Generalized \(m\)-preinvexity on fractal set and related local fractional integral inequalities with applications
Generalized \(m\)-preinvexity on fractal set and related local fractional integral inequalities with applications
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In this work, we address and explore the concept of generalized \(m\)-preinvex functions on fractal sets along with linked local fractional integral inequalities. Additionally, some engrossing algebraic properties are presented to facilitate the current initiated idea. Furthermore, we prove the latest variant of Hermite-Hadamard type inequality employing the proposed definition of preinvexity. We also derive several novel versions of inequalities of the Hermite-Hadamard type and Fejér-Hermite-Hadamard type for the first-order local differentiable generalized \(m\)-preinvex functions. Finally, some new inequalities for the generalized means and generalized random variables are established as applications.
352
371
S.
Al-Sa'di
Department of Mathematics, Faculty of Science
The Hashemite University
Jordan
saud@hu.edu.jo
M.
Bibi
Department of Basics Sciences
University of Engineering and Technology
Pakistan
mariabibi782@gmail.com
M.
Muddassar
Department of Basics Sciences
University of Engineering and Technology
Pakistan
muhammad.mudassar@uettaxila.edu.pk
S.
Kermausuor
Department of Mathematics and Computer Science
Alabama State University
USA
skermausour@alasu.edu
Generalized \(m\)-preinvex functions
generalized Hermite-Hadamard inequality
generalized Fejér-Hermite-Hadamard type inequality
fractal sets
fractional integral inequalities
Article.5.pdf
[
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Generalised Hermite-Hadamard type inequalities for \((s,r)\)-convex functions in mixed kind with applications
Generalised Hermite-Hadamard type inequalities for \((s,r)\)-convex functions in mixed kind with applications
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In this article, some generalized inequalities of the Hermite-Hadamard type for functions whose modulus of the derivatives are \((s,r)\)-convex in mixed kind and applications for probability theory and numerical integration are given. Various established results of different articles would be recaptured as special cases. We also provide special cases of the class of \((s,r)\)-convex function on several choices of \(s,r\).
372
380
F.
Mehmood
Department of Mathematics
Department of Mathematics
Samarkand State University
Dawood University of Engineering and Technology
Uzbekistan
Pakistan
faraz.mehmood@duet.edu.pk
F.
Nawaz
Department of Mathematics
Dawood University of Engineering and Technology
Pakistan
mirhafaisal@yahoo.com
A.
Soleev
Department of Mathematics
Samarkand State University
Uzbekistan
asoleev@yandex.ru
Convex function
Hermite-Hadamard inequality
Hölder inequality
power-mean inequality
numerical integration
probability density function
Article.6.pdf
[
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On the elliptical solutions of models connected to the short pulse equation
On the elliptical solutions of models connected to the short pulse equation
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In the present paper, we
consider a special hierarchy of equations comprising the short pulse equation, the sine-Gordon integrable hierarchy and the elastic beam equation. These equations are highly non-linear and rely on transformations to arrive at solutions. Previously, recursion operators and hodograph mappings were successful in reducing these equations. However, we show that via the
conservation laws or the one-parameter Lie group, the special hierarchy may be integrated and will admit the exact solutions that feature elliptical functions.
381
389
S.
Jamal
School of Mathematics
University of the Witwatersrand
South Africa
sameeerah.Jamal@wits.ac.za
R.
Champala
School of Mathematics
University of the Witwatersrand
South Africa
Lie symmetries
elastic beam equations
sine-Gordon
Article.7.pdf
[
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Analysis of a malaria transmission mathematical model considering immigration
Analysis of a malaria transmission mathematical model considering immigration
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The aims of this paper are to study the local and global stability of the equilibrium points using a mathematical model for malaria disease. The model is based on five differential equations. The analysis of the stability was examined using the Lyapunov method. We prove that the disease free equilibrium point is locally and globally asymptotically stable when \(R_0<1\) and unstable when \(R_0>1\). On the other hand, the endemic equilibrium point is locally and globally asymptotically stable when \(R_0>1\).
390
406
C.
Taftaf
Lab-Mia, Faculty of Sciences
Mohammed V University in Rabat
Morocco
taftaf.chaimaa@gmail.com
H.
Benazza
Lab-Mia, Faculty of Sciences
Mohammed V University in Rabat
Morocco
Y.
Louartassi
Superior School of Technology Sale
Mohammed V University in Rabat
Morocco
Z.
Hamidi
Laboratory M2PA, Department of mathematics \(\&\) informatics
ENS. University Sidi Mohamed Ben Abdellah. Fez
Morocco
Malaria
epidemic model
Lyapunov
endemic equilibrium
disease-free equilibrium
Article.8.pdf
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