Matematik Bölümü Yayın Koleksiyonu

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Subject: search.filters.subject.Existence And Uniqueness

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  • Article
    Citation - WoS: 51
    Citation - Scopus: 66
    Existence and Uniqueness of Solutions to Fractional Differential Equations in the Frame of Generalized Caputo Fractional Derivatives
    (Springer, 2018) Gambo, Y. Y.; Ameen, R.; Jarad, Fahd; Abdeljawad, T.
    The generalized Caputo fractional derivative is a name attributed to the Caputo version of the generalized fractional derivative introduced in Jarad et al. (J. Nonlinear Sci. Appl. 10:2607-2619, 2017). Depending on the value of. in the limiting case, the generality of the derivative is that it gives birth to two different fractional derivatives. However, the existence and uniqueness of solutions to fractional differential equations with generalized Caputo fractional derivatives have not been proven. In this paper, Cauchy problems for differential equations with the above derivative in the space of continuously differentiable functions are studied. Nonlinear Volterra type integral equations of the second kind corresponding to the Cauchy problem are presented. Using Banach fixed point theorem, the existence and uniqueness of solution to the considered Cauchy problem is proven based on the results obtained.
  • Article
    Citation - Scopus: 1
    Existence Results for an Impulsive Pantograph Differential Equations Within Exponential Kernel
    (Univ Politehnica Bucharest, Sci Bull, 2022) Kavitha, Velusamy; Baleanu, Dumitru; Kanimozhi, Palanisamy; Arjunan, Mani Mallika; Baleanu, Dumitru; Matematik
    This manuscript deals with the existence results for an impulsive pantograph integro-differential equations (IPIDE) through Caputo-Fabrizio (CF) operator. Certain novel existence findings are shown using fixed point approaches. Finally, two numerical examples are provided in the work to demonstrate the application of our theoretical findings.
  • Article
    Citation - WoS: 7
    Analysis O a Caputo Hiv and Malaria Co-Infection Epidemic Model
    (Chiang Mai Univ, Fac Science, 2021) Ahmed, Idris; Jarad, Fahd; Yusuf, Abdullahi; Sani, Musbahu Aminu; Jarad, Fahd; Kumam, Wiyada; Thounthong, Phatiphat; Matematik
    In this paper, we investigate a fractional-order compartmental HIV and Malaria co-infection epidemic model using the Caputo derivative. The existence and uniqueness of the solution to the proposed fractional-order model were investigated using fixed point theorem techniques. To demonstrate that the proposed fractional-order model is both mathematically and epidemiologically well-posed, we compute the model's positivity and boundedness, which is an important feature in epidemiology. Finally, we analyze the dynamic behavior of each of the state variables using a recent and powerful computational technique known as the fractional Euler method.
  • Article
    Citation - Scopus: 55
    Nonlinear Delay Fractional Difference Equations With Applications on Discrete Fractional Lotka–volterra Competition Model
    (Eudoxus Press, LLC, 2018) Abdeljawad, Thabet; Alzabut, J.; Abdeljawad, T.; Baleanu, Dumitru; Baleanu, D.; Matematik
    The existence and uniqueness of solutions for nonlinear delay fractional difference equations are investigated in this paper. We prove the main results by employing the theorems of Krasnoselskii’s Fixed Point and Arzela–Ascoli. As an application of the main theorem, we provide an existence result on the discrete fractional Lotka–Volterra model. ©2018 by Eudoxus Press, LLC. All rights reserved.
  • Article
    Citation - WoS: 10
    Citation - Scopus: 10
    Novel 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, Saima
    Because 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: 9
    Citation - Scopus: 11
    Monkeypox 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 pal
    A 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 - Scopus: 14
    A Fractional Order Co-Infection Model Between Malaria and Filariasis Epidemic
    (Taylor and Francis Ltd., 2024) Kumar, A.; Kumar, S.; Baleanu, D.; Kumar, P.
    In this article, we investigate a mathematical malaria-filariasis co-infection model with the assistance of the non-integer order operator. Using the fractal-fractional operator in the Caputo-Fabrizio (CF) sense, it has been possible to understand the dynamical behaviour and complicatedness of the malaria-filariasis model. An investigation of the existence and uniqueness of the solution employs fixed-point theory. Ulam-Hyers stability helps examine the stability analysis of the proposed co-infection model. The malaria-filariasis model has been investigated using the Toufik-Atanagana (TA), a sophisticated numerical method for these biological co-infection models. With the help of numerical procedures, we provide the approximate solutions for the proposed model. A variety of fractal dimension and fractional order options are utilized for the presentation of the results. When we adjust sensitive parameters like τ and γ, the graphical representation illustrates the system’s behaviour and identifies suitable parameter ranges for solutions. In addition, we evaluate the model along with the regarded operators and various β1 values using an exceptional graphical representation. © 2024 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the University of Bahrain.
  • Article
    Citation - WoS: 19
    Citation - Scopus: 22
    Numerical 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, Saima
    The 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: 50
    Citation - Scopus: 55
    Numerical 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: 7
    Citation - Scopus: 8
    Numerical 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 Abdullahi
    In 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.