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2025
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Exploring COVID-19 model with general fractional derivatives: novel Physics-Informed-Neural-Networks approach for dynamics and order estimation
Exploring COVID-19 model with general fractional derivatives: novel Physics-Informed-Neural-Networks approach for dynamics and order estimation
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en
In this paper, a fractional coronavirus disease model including unreported cases is suggested. The considered model includes a general fractional derivative incorporating well-known types, specifically Caputo-Fabrizio, Atangana-Baleanu and Weighted Atangana-Baleanu. Our theoretical results are two-fold. First, under suitable assumptions, the existence of a solution for the considered system is proven. Moreover, the local stability of the free-disease and endemic equilibrium points is addressed in terms of \(R_{0}\). Secondly, a particular example is considered where the fractional derivative has two varying parameters, and an approach allowing for their estimation is proposed, with the aim of providing the best approximation of the real COVID-19 dynamics. The main novelty of our proposed approach is its use of physics-informed-neural-networks (PINNs) for estimating the fractional orders. On the other hand, to validate our results, a numerical simulations are conducted to illustrate the local stability of the disease dynamics, as well as the effectiveness of our proposed method in providing the best approximation of the two fractional derivative parameters.
142
162
H.
Aghdaoui
MAIS Laboratory, MAMCS Group, FST Errachidia
Moulay Ismail University of Meknes
Morocco
A. A.
Raezah
Department of Mathematics, Faculty of Science
King Khalid University
Saudi Arabia
M.
Tilioua
MAIS Laboratory, MAMCS Group, FST Errachidia
Moulay Ismail University of Meknes
Morocco
Y.
Sabbar
MAIS Laboratory, MAMCS Group, FST Errachidia
Moulay Ismail University of Meknes
Morocco
y.sabbar@umi.ac.ma
Epidemic model
incidence rate
equilibrium points
optimal control
numerical analysis
Article.1.pdf
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]
Exploring lock-down effects in a fractional order Covid-19 model with crossover behavior
Exploring lock-down effects in a fractional order Covid-19 model with crossover behavior
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en
This research article delves into the intricate dynamics of a COVID-19 model, uniquely characterized by the integration of lock-down measures through a piecewise operator that encompasses both classical and Caputo operators. The article not only examines the model's behavior but also rigorously establishes the existence and uniqueness of solutions for this complex piecewise system. To tackle the numerical approximation of solutions, the study employs Newton's polynomial interpolation scheme, shedding light on the model's behavior under different conditions. Through meticulous graphical representations, the article effectively communicates the results and numerical solutions across various classes of the model, each defined by distinct fractional orders. This comprehensive approach provides valuable insights into the pandemic's multifaceted dynamics, serving as a basis for understanding its progression and evaluating potential control strategies.
163
174
M. A.
El-Shorbagy
Department of Mathematics, College of Science and Humanities in Al-Kharj
Department of Basic Engineering Science, Faculty of Engineering
Prince Sattam bin Abdulaziz University
Menoufia University
Saudi Arabia
Egypt
ma.hassan@psau.edu.sa
COVID-19
fractional operator
existence and uniqueness
stability analysis
numerical simulations
Article.2.pdf
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]
The dynamics in an intraguild prey-predator model with Holling type III functional response
The dynamics in an intraguild prey-predator model with Holling type III functional response
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en
In prey-predator models, nonlinear interaction between prey and predator populations results in oscillatory behavior that shows the dynamic growth of the populations. In the growth process, very often both prey and predator share the same resource in their habitat. This is an intraguild predation model. This study focuses on an intraguild prey-predator model generalized by introducing Holling type III functional response. The existence of biologically meaningful equilibria has been investigated. The stability analysis of the equilibria has been determined. Finally, bifurcation and numerical analyses have been presented to illustrate the dynamic behavior of the system. Taking the {biotic resource enrichment as the bifurcation parameter}, a Hopf bifurcation takes place, where solutions with limit cycle behavior appear. Varying further the parameter, a fold bifurcation of the limit cycle takes place, where the unstable limit appeared due to Hopf bifurcation reverses its growing direction and changes its stability. Taking the predation rate as the {bifurcation parameter}, saddle-node bifurcations take place. The existence of stable interior equilibria and stable periodic solutions, of which all prey and predator populations and the resource co-exist, guarantee the boundedness of the size of the populations and the resource. This is good from the conservation of an ecosystem point of view.
175
184
Abadi
Mathematics Department, Faculty of Mathematics and Natural Sciences
Universitas Negeri Surabaya
Indonesia
abadi@unesa.ac.id
D.
Savitri
Mathematics Department, Faculty of Mathematics and Natural Sciences
Universitas Negeri Surabaya
Indonesia
F.
Adi-Kusumo
Mathematics Department, Faculty of Mathematics and Natural Sciences
Universitas Gadjah Mada
Indonesia
Intraguild
prey
predator
stability
bifurcation
Article.3.pdf
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]
Giardiasis transmission dynamics: insights from fractal-fractional modeling and deep neural networks
Giardiasis transmission dynamics: insights from fractal-fractional modeling and deep neural networks
en
en
The World Health Organization highlights Giardias as a neglected zoonotic disease caused by Giardia duodenalis. The disease often goes overlooked despite the significant harm it causes humans and animals. We present a mathematical model for transmitting Giardiasis incorporating various preventative measures, including screening, treatment, and environmental sanitation. Among the factors influencing Giardiasis transmission within a community is the interaction parameter between humans and the environment.
In this manuscript, Atangana-Baleanu Caputo (ABC) derivatives of fractional order \(v\) and fractal dimension \(q\) are utilized to explore a modified model with a fractal-fractional approach. The study qualitatively analyses the model using functional non-linearity and population-based fixed-point theory. The fractional Adams-Bashforth iterative method is used to obtain numerical solutions. Ulam-Hyers (UH) stability techniques are used to analyze stability in this study. A comparison is made between simulation results for all compartments and Giardia duodenalis data already available. To manage Giardiasis duodenalis effectively, societal behavioral changes and adherence to preventive measures are essential to controlling the effective transmission rate. Additionally, a deep neural network (DNN) approach is used to analyze the given disease condition with excellent accuracy in training, testing, and validation data.
185
206
M. A.
El-Shorbagy
Department of Mathematics, College of Science and Humanities in Al-Kharj
Department of Basic Engineering Science, Faculty of Engineering
Prince Sattam bin Abdulaziz University
Menoufia University
Saudi Arabia
Egypt
S.
Tabussam
Department of Applied Sciences
National Textile University
Pakistan
M. u.
Rahman
School of Mathematical Sciences
Department of computer science and mathematics
Jiangsu University
Lebanese American University
P.R. China
Lebanon
matiur.Rahman@lau.edu.lb
Waseem
School of Mechnical Engineering
Jiangsu University
P.R. China
Giardiasis duodenalis
existence result
fractal-fractional ABC operator
deep neural network
numerical results
Article.4.pdf
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Theoretical and computational results for implicit non-singular hybrid fractional differential equation subject to multi-terms non-local initial conditions
Theoretical and computational results for implicit non-singular hybrid fractional differential equation subject to multi-terms non-local initial conditions
en
en
This research work is devoted to investigate a class of hybrid fractional differential equations with \(n+1\) terms initial conditions. The aforesaid problem is considered under the Atangana-Baleanue-Caputo fractional order derivative. Here it is remarkable that hybrid differential equations with linear perturbations have significant applications in modeling various dynamical problems. Sufficient conditions are established for the existence and uniqueness of solution to the problem under investigation by using the Banach and Krasnoselsikii's fixed point theorems. Since stability theory plays important role in establishing various numerical and optimizations results, therefore, Hyers-Ulam type stability results are deduced for the considered problems using the tools of nonlinear functional analysis. Additionally, a numerical method based on Euler procedure is established to study some approbation results for the proposed problem. By a pertinent example, we demonstrate our results. Also some graphical illustrations for different fractional orders are given.
207
217
Shafiullah
Department of Mathematics
University of Malakand
Pakistan
K.
Shah
Department of Mathematics
Department of Mathematics and Sciences
University of Malakand
Prince Sultan University
Pakistan
Saudi Arabia
kamalshah408@gmail.com
M.
Sarwar
Department of Mathematics
Department of Mathematics and Sciences
University of Malakand
Prince Sultan University
Pakistan
Saudi Arabia
Th.
Abdeljawad
Department of Mathematics and Sciences
Prince Sultan University
Saudi Arabia
tabdeljawad@psu.edu.sa
Atangana-Baleanu Caputo derivative
Hyers-Ulam stability
fixed point theorem
Euler numerical method
Article.5.pdf
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]
Computational framework for analyzing fractional biochemical reaction model
Computational framework for analyzing fractional biochemical reaction model
en
en
The approximate numerical approach for the system of coupled nonlinear ordinary differential equations (ODEs) of a biochemical reaction model is very important for biochemists and scientist working in the field of biochemistry and related issues. Within this article, two computational algorithms for numerically solving a biochemical reaction model with time-fractional derivatives are examined and compared. The first technique depends on the collocation method along with the shifted Jacobi operational matrix for fractional derivative defined in the Caputo sense, and using this technique, we created a system of algebraic equations from the given fractional model. Another approach is centered on the basic theorem of fractional calculus and the characteristics of Newton's polynomial interpolation (NPI). We use these two methods to compute solution for the fractional biochemical reaction model. The model's computational outcomes are compared by using the recommended techniques in this work. Graphical and tabular forms are used to confirm the reliability and effectiveness of both techniques and an excellent match is discovered.
218
228
D.
Kumar S
Department of Mathematics
Department of Mathematics
University of Rajasthan
Kyung Hee University
India
Korea
devendra.maths@gmail.com
H.
Nama
Department of Mathematics
University of Rajasthan
India
namahunney99@gmail.com
D.
Baleanu
Department of Computer Science and Mathematics
Institute of Space Sciences-Subsidiary of INFLPR
Lebanese American University
Lebanon
Romania
dumitru.baleanu@gmail.com
Biochemical reaction model
collocation technique
Newton polynomial interpolation
Jacobi operational matrix
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Hyers-Ulam stability of a-type additive functional equations in Banach space using direct method
Hyers-Ulam stability of a-type additive functional equations in Banach space using direct method
en
en
In this paper, we introduce the new kind of a-type additive functional equation and investigate the Hyers-Ulam stability of a-type additive functional equations within the Banach spaces using the direct method. This approach provides a straightforward and efficient way to establish the stability of functional equations without relying on more complex or indirect techniques. We begin by defining the specific a-type additive functional equation under consideration and outlining the conditions required for its stability. Through rigorous mathematical analysis, we demonstrate that under certain constraints, the functional equation exhibits Hyers-Ulam stability.
229
236
P.
Karthick
Department of Mathematics
Government Arts College for Men
India
www.ksk2015@gmail.com
G.
Balasubramanian
Department of Mathematics
Government Arts College for Men
India
gbs_geetha@yahoo.com
V.
Govindan
Department of Mathematics,
Hindustan Institute of Technology and Science
India
govindoviya@gmail.com
M. I.
Khan
Department of Mechanical Engineering, College of Engineering
Prince Mohammed bin Fahd University
Kingdom of Saudi Arabia
mkhan1@pmu.edu.sa
J. L.
Amalraj
Department of Science and Humanities
RMK College of Engineering and Technology
India
leoamalraj@rmkcet.ac.in
A. J.
Bala
Department of Mathematics
R.M.D. Engineering College
India
jothibala.snh@rmd.ac.in
Additive functional equation
Banach space
direct method
Hyers-Ulam stability
Article.7.pdf
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]
Strongly bounded variation functions in Krein spaces
Strongly bounded variation functions in Krein spaces
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en
In the present paper we introduce the notion of strongly bounded variation function in Krein spaces, we show that the definition of bounded variation is independent of the decomposition of the Krein space and the definition of bounded variation of a function in Hilbert spaces given in [V. V. Chistyakov, J. Dynam. Control Syst., \(\textbf{3}\) (1997), 261--289], is a particular case of the one introduced in this paper. We show a technique for constructing bounded variation functions on Krein spaces from bounded variation functions on the Hilbert subspaces composing the Krein space.
237
250
O. F.
Villar
University of Sucre. Cra. 28\#5-26
Colombia
osmin.ferrer@unisucre.edu.co
J. N.
Martinez
Center for Basic Sciences, School of Engineering and Architecture
Pontifical Bolivarian University
Colombia
C. G.
Mestra
University of Sucre. Cra. 28\#5-26
Colombia
Indefinite metric
Krein space
bounded variation
negative variation
Article.8.pdf
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]