Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
Browse
19 results
Search Results
Article Citation - WoS: 10Citation - Scopus: 10Novel Investigation of Stochastic Fractional Differential Equations Measles Model Via the White Noise and Global Derivative Operator Depending on Mittag-Leffler Kernel(Tech Science Press, 2024) Jarad, Fahd; Rashid, SaimaBecause of the features involved with their varied kernels, differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real -world issues. In this paper, we constructed a stochastic fractional framework of measles spreading mechanisms with dual medication immunization considering the exponential decay and Mittag-Leff ler kernels. In this approach, the overall population was separated into five cohorts. Furthermore, the descriptive behavior of the system was investigated, including prerequisites for the positivity of solutions, invariant domain of the solution, presence and stability of equilibrium points, and sensitivity analysis. We included a stochastic element in every cohort and employed linear growth and Lipschitz criteria to show the existence and uniqueness of solutions. Several numerical simulations for various fractional orders and randomization intensities are illustrated.Article Citation - WoS: 9Citation - Scopus: 11Monkeypox Viral Transmission Dynamics and Fractional-Order Modeling With Vaccination Intervention(World Scientific Publ Co Pte Ltd, 2023) Kumar, Sachin; Baleanu, Dumitru; Nisar, Kottakkaran sooppy; Singh, Jaskirat palA current outbreak of the monkeypox viral infection, which started in Nigeria, has spread to other areas of the globe. This affects over 28 nations, including the United Kingdom and the United States. The monkeypox virus causes monkeypox (MPX), which is comparable to smallpox and cowpox (MPXV). The monkeypox virus is a member of the Poxviridae family and belongs to the Orthopoxvirus genus. In this work, a novel fractional model for Monkeypox based on the Caputo derivative is explored. For the model, two equilibria have been established: disease-free and endemic equilibrium. Using the next-generation matrix and Castillo's technique, if R-0 < 1 the global asymptotic stability of disease-free equilibrium is shown. The linearization demonstrated that the endemic equilibrium point is locally asymptotically stable if R-0 > 1. Using the parameter values, the model's fundamental reproduction rates for both humans and non-humans are calculated. The existence and uniqueness of the solution are proved using fixed point theory. The model's numerical simulations demonstrate that the recommended actions will cause the infected people in the human and non-human populations to disappear.Article Citation - WoS: 19Citation - Scopus: 22Numerical Investigation of Fractional-Order Cholera Epidemic Model With Transmission Dynamics Via Fractal-Fractional Operator Technique(Pergamon-elsevier Science Ltd, 2022) Jarad, Fahd; Alsharidi, Abdulaziz Khalid; Rashid, SaimaThe goal of this research is to determine if it is conceptually sufficient to eliminate infection in a community by utilizing mathematical modelling and simulation techniques when appropriate protective controls are adopted. In this research, we investigate the straightforward interaction transmission method to create a deterministic mathematical formulation of cholera infectious dynamics via the fractal-fractional (F-F) derivative operator. Furthermore, the qualitative characteristics of the framework are investigated, including the invariant region, the existence of a positive invariant solution, the equilibria conditions and their stabilities. In addition, the fundamental reproductive number R-0 < 1 is calculated, indicating that the strategy is more plausible. The Atangana-Baleanu, Caputo-Fabrizio, and Caputo F-F differential operators are recently described F-F differential operators that are used to describe the computational formula of the cholera epidemic model. We examined the numerical dynamics of the cholera epidemic, considering three assumptions: (i) altering fractal order while fixing fractional order; (ii) changing fractional order while fixing fractal order; and (iii) fluctuating fractal and fractional orders simultaneously. For the numerical modelling of the aforesaid model, our analysed graphical representations and numerical simulations via MATLAB indicate that the newly proposed Atangana-Baleanu, Caputo-Fabrizio, and Caputo F-F differential operators yield notable outcomes when compared to the classical framework. According to the simulated data, reduced contact rate, successful recovery rate, and appropriate hygiene are the most essential aspects for eliminating cholera disease from the community.Article Citation - WoS: 50Citation - Scopus: 55Numerical Analysis of Atangana-Baleanu Fractional Model To Understand the Propagation of a Novel Corona Virus Pandemic(Elsevier, 2022) Butt, A. I. K.; Ahmad, W.; Rafiq, M.; Baleanu, D.In this manuscript, we formulated a new nonlinear SEIQR fractional order pandemic model for the Corona virus disease (COVID-19) with Atangana-Baleanu derivative. Two main equilibrium points F-0*, F-1* of the proposed model are stated. Threshold parameter R-0 for the model using next generation technique is computed to investigate the future dynamics of the disease. The existence and uniqueness of solution is proved using a fixed point theorem. For the numerical solution of fractional model, we implemented a newly proposed Toufik-Atangana numerical scheme to validate the importance of arbitrary order derivative q and our obtained theoretical results. It is worth mentioning that fractional order derivative provides much deeper information about the complex dynamics of Corona model. Results obtained through the proposed scheme are dynamically consistent and good in agreement with the analytical results. To draw our conclusions, we explore a complete quantitative analysis of the given model for different quarantine levels. It is claimed through numerical simulations that pandemic could be eradicated faster if a human community selfishly adopts mandatory quarantine measures at various coverage levels with proper awareness. Finally, we have executed the joint variability of all classes to understand the effectiveness of quarantine policy on human population. (c) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/ 4.0/).Article Citation - WoS: 7Citation - Scopus: 8Numerical and Theoretical Analysis of an Awareness Covid-19 Epidemic Model Via Generalized Atangana-Baleanu Fractional Derivative(Czestochowa Univ Technology, inst Mathematics, 2022) Ahmed, Idris; Al-Mdallal, Qasem M.; Jarad, Fahd; Yunusa, Salisu; Baba, Isa AbdullahiIn this paper, a COVID-19 Awareness model in the setting of a generalized fractional Atangana-Baleanu derivative is proposed. The existence and uniqueness of a solution of the proposed fractional-order model are investigated under the techniques of fixed point theorems. In addition, we perform the predictor-corrector method to find its numeric solutions and present the graphs of the various solutions using different values of the parameters embodied in the derivative.Article Citation - WoS: 5Citation - Scopus: 8Predictive Dynamical Modeling and Stability of the Equilibria in a Discrete Fractional Difference Covid-19 Epidemic Model(Elsevier, 2023) Rashid, Saima; Akdemir, Ahmet Ocak; Khalid, Aasma; Baleanu, Dumitru; Al-Sinan, Bushra R.; Elzibar, O. A. I.; Chu, Yu-MingThe SARSCoV-2 virus, also known as the coronavirus-2, is the consequence of COVID-19, a severe acute respiratory syndrome. Droplets from an infectious individual are how the pathogen is transmitted from one individual to another and occasionally, these particles can contain toxic textures that could also serve as an entry point for the pathogen. We formed a discrete fractional-order COVID-19 framework for this investigation using information and inferences from Thailand. To combat the illnesses, the region has implemented mandatory vaccination, interpersonal stratification and mask distribution programs. As a result, we divided the vulnerable people into two groups: those who support the initiatives and those who do not take the influence regulations seriously. We analyze endemic problems and common data while demonstrating the threshold evolution defined by the fundamental reproductive quantity R0. Employing the mean general interval, we have evaluated the configuration value systems in our framework. Such a framework has been shown to be adaptable to changing pathogen populations over time. The Picard Lindelof technique is applied to determine the existence-uniqueness of the solution for the proposed scheme. In light of the relationship between the R0 and the consistency of the fixed points in this framework, several theoretical conclusions are made. Numerous numerical simulations are conducted to validate the outcome.Article Citation - WoS: 3Citation - Scopus: 3Existence and Stability Analysis for Caputo Generalized Hybrid Langevin Differential Systems Involving Three-Point Boundary Conditions(Springer, 2023) Matar, Mohammed M.; Abdeljawad, Thabet; Jarad, Fahd; Boutiara, A.This research inscription gets to grips with two novel varieties of boundary value problems. One of them is a hybrid Langevin fractional differential equation, whilst the other is a coupled system of hybrid Langevin differential equation encapsuling a collective fractional derivative known as the psi-Caputo fractional operator. Such operators are generated by iterating a local integral of a function with respect to another increasing positive function psi. The existence of the solutions of the aforehand equations is tackled by using the Dhage fixed point theorem, whereas their uniqueness is handled using the Banach fixed point theorem. On the top of this, the stability within the scope of Ulam-Hyers of solutions to these systems are also considered. Two pertinent examples are presented to corroborate the reported results.Article Citation - WoS: 107Citation - Scopus: 107Dynamics Exploration for a Fractional-Order Delayed Zooplankton-Phytoplankton System(Pergamon-elsevier Science Ltd, 2023) Gao, Rong; Xu, Changjin; Li, Ying; Akgul, Ali; Baleanu, Dumitru; Li, PeiluanIn this study, we are concerned with the dynamics of a new established fractional-order delayed zooplankton- phytoplankton system. The existence and uniqueness of the solution are proved via Banach fixed point theorem. Non-negativeness of the solution is studied by mathematical inequality technique. The boundedness of the solution is analyzed by virtue of constructing an appropriate function. A novel delay-independent sufficient condition ensuring the stability and the onset of Hopf bifurcation for the established fractional -order delayed zooplankton-phytoplankton system is derived by means of Laplace transform, stability criterion and bifurcation knowledge of fractional-order differential equation. The global stability condition for the involved fractional-order delayed zooplankton-phytoplankton system is built by using a suitable positive definite function. Taking advantage of hybrid control tactics, we effectively control the time of occurrence of Hopf bifurcation for the established fractional-order delayed zooplankton-phytoplankton system. The study manifests that delay plays a vital role in controlling the stability and the time of occurrence of Hopf bifurcation for the involved fractional-order delayed zooplankton-phytoplankton system and the fractional -order controlled zooplankton-phytoplankton system involving delays. To verify the correctness of established chief results, computer simulation figures are distinctly displayed. The derived conclusions of this research are entirely new and possess potential theoretical value in preserving the balance of biological population. Up to now, there are few publications on detailed and comprehensive dynamic analysis on fractional-order delayed zooplankton-phytoplankton system via various exploration ways.Article Citation - WoS: 18Citation - Scopus: 20Comprehending the Model of Omicron Variant Using Fractional Derivatives(Taylor & Francis Ltd, 2023) Goswami, Pranay; Baleanu, Dumitru; Shankar Dubey, Ravi; Sharma, ShivaniThe world is grappled with an unprecedented challenges due to Corona virus. We are all battling this epidemic together, but we have not been able to defeat this epidemic yet. A new variant of this virus, named 'Omicron' is spreading these days. The fractional differential equations are providing us with better tools to study the mathematical model with memory effects. In this paper, we will consider an extended SER mathematical model with quarantined and vaccinated compartment to speculate the Omicron variant. This extended Susceptible Exposed Infected Recovered SER model involves equations that associate with the group of individuals those are susceptible (S), exposed (E): this class includes the individuals who are infected but not yet infectious, infectious (W): this class includes the individuals who are infected but not yet Quarantined, quarantined (Q): this class includes those group of people who are infectious, confirmed and quarantined, recovered (R) this class includes the group of individuals who have recovered, and vaccinated (V): this class includes the group of individuals who have been vaccinated. The non-negativity and of the extended SER model is analysed, the equilibrium points and the basic reproduction number are also calculated. The proposed model is then extended to the mathematical model using AB derivative operator. Proof for the existence and the uniqueness for the solution of fractional mathematical model in sense of AB fractional derivative is detailed and a numerical method is detailed to obtain the numerical solutions. Further we have discussed the efficiency of the vaccine against the Omicron variant via graphical representation.Article Citation - WoS: 144Citation - Scopus: 158Semi-Analytical Study of Pine Wilt Disease Model With Convex Rate Under Caputo-Febrizio Fractional Order Derivative(Pergamon-elsevier Science Ltd, 2020) Jarad, Fahd; Abdeljawad, Thabet; Shah, Kamal; Alqudah, Manar A.In this paper, we present semi-analytical solution to Pine Wilt disease (PWD) model under the CaputoFabrizio fractional derivative (CFFD). For the proposed solution, we utilize Laplace transform coupled with Adomian decomposition method abbreviated as (LADM). The concerned method is a powerful tool to obtain semi-analytical solution for such type of nonlinear differential equations of fractional order (FODEs) involving non-singular kernel. Furthermore, we give some results for the existence of solution to the proposed model and present numerical results to verify the established analysis. (C) 2020 Elsevier Ltd. All rights reserved.