Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Subject: search.filters.subject.Fixed Point Theorems

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  • Article
    Citation - Scopus: 9
    A Dynamical and Sensitivity Analysis of the Caputo Fractional-Order Ebola Virus Model: Implications for Control Measures
    (Thammasat University, 2023) Ahmed, I.; Jarad, Fahd; Yusuf, A.; Tariboon, J.; Muhammad, M.; Jarad, F.; Mikailu, B.B.; Matematik
    The recurrence of outbreaks in cases of Ebola virus among African countries remains one of the greatest issues of concern. Practices such as hunting or consumption of contam-inated bush meat, unsafe funeral practices, and environmental contamination have all been implicated as possible contributors. This paper investigates the transmission dynamics of the Ebola virus model in the setting of a Caputo fractional-order derivative that accounts for both direct and indirect transmissions of the virus. By employing the concept of fixed theorems, we derived the existence and uniqueness results of the model. Moreover, we analyzed the forward normalized sensitivity indices to identify the critical parameters for controlling the infection and found that reducing the contact rate between infected individuals and susceptible vectors is vital to limiting the virus’s spread. Comparing the proposed fractional-order model with those of the previously developed integer-order model numerically, we found that the proposed model provides more reliable information on the model’s dynamics. Thus, we conclude that the Caputo fractional-order operator is a precise tool for describing the proposed model behavior and can help understand the complexities of Ebola virus disease outbreaks. © 2023, Thammasat University. All rights reserved.
  • Article
    Citation - Scopus: 1
    Qualitative Analysis of Nonlinear Hilfer Fractional Implicit Differential Equations in a Banach Space
    (DergiPark, 2023) Dhawan, K.; Vats, R.K.; Karapinar, E.
    This article focuses on the class of nonlinear implicit Hilfer-type fractional differential equations. By using the non-linear growth condition, we have derived the existence of at least one solution by applying Schauder’s fixed point theorem and using Lipschitz conditions, we have derived the uniqueness of the solution with the help of the Banach contraction principle. In addition, we have discussed the stability analysis by using Ulam-Hyers and Ulam-Hyers-Rassias stabilities. All results of this paper are established in a Banach space instead of R. We illustrate our results with the help of two examples. © 2023, DergiPark. All rights reserved.
  • Article
    Sequences of Nonlinear Quasi Contractions and Fixed Points
    (Univ Nis, Fac Sci Math, 2022) Chi, Kieu Phuong; Karapinar, Erdal; Thanh, Tran Duc
    In this paper, we state some results on the relationship between the convergence of the nonlinear quasi-contractions and the convergence of their fixed point. The observed results certainly extend some existing results on the topic in the literature, including the results of Nadler and Park. We also furnish an illustrative example to demonstrate the validity of the results expressed.
  • 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.
  • Article
    Citation - Scopus: 2
    On Abstract Cauchy Problems in the Frame of a Generalized Caputo Type Derivative
    (DergiPark, 2023) Adjabi, Y.; Abdeljawad, T.; Mahariq, I.; Bourchi, S.; Jarad, F.
    In this paper, we consider a class of abstract Cauchy problems in the framework of a generalized Caputo type fractional. We discuss the existence and uniqueness of mild solutions to such a class of fractional differential equations by using properties found in the related fractional calculus, the theory of uniformly continuous semigroups of operators and the fixed point theorem. Moreover, we discuss the continuous dependence on parameters and Ulam stability of the mild solutions. At the end of this paper, we bring forth some examples to endorse the obtained results. © 2023, DergiPark. All rights reserved.
  • Article
    Citation - WoS: 4
    Citation - Scopus: 3
    A Fixed Point Theorem for Proinov Mappings With a Contractive Iterate
    (Zhejiang Univ Press, 2023) Fulga, Andreea; Karapinar, Erdal
    In this paper, we consider the fixed point theorem for Proinov mappings with a contractive iterate at a point. In other words, we combine and unify the basic approaches of Proinov and Sehgal in the framework of the complete metric spaces. We consider examples to illustrate the validity of the obtained result.
  • Book Part
    Citation - Scopus: 3
    Revisiting Fixed Point Results With a Contractive Iterative at a Point
    (Springer Science and Business Media Deutschland GmbH, 2021) Karapinar, E.
    In this manuscript, we shall discuss fixed point results with a contractive iterative at a point in the setting of various abstract space. The first aim of this paper is to collect the corresponding basic results on the topic in the literature. After then, our purpose is to combine and connect several existing results in this direction by generalizing the famous theorem of Matkowski. We shall consider some consequence of our main result to illustrate its genuineness. © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.
  • Article
    Citation - WoS: 3
    Citation - Scopus: 3
    Quadruple Fixed Point Theorems for Nonlinear Contractions on Partial Metric Spaces
    (Univ Politecnica Valencia, Editorial Upv, 2014) Karapinar, Erdal; Tas, Kenan
    The notion of coupled fixed point was introduced by Guo and Laksmikantham [12]. Later Gnana Bhaskar and Lakshmikantham in [11] investigated the coupled fixed points in the setting of partially ordered set by defining the notion of mixed monotone property. Very recently, the concept of tripled fixed point was introduced by Berinde and Borcut [7]. Following this trend, Karapmar[19] defined the quadruple fixed point. In this manuscript, quadruple fixed point is discussed and some new fixed point theorems are obtained on partial metric spaces.
  • Article
    Citation - WoS: 56
    Citation - Scopus: 67
    On Hilfer Generalized Proportional Fractional Derivative
    (Springer, 2020) Kumam, Poom; Jarad, Fahd; Borisut, Piyachat; Jirakitpuwapat, Wachirapong; Ahmed, Idris
    Motivated by the Hilfer and the Hilfer-Katugampola fractional derivative, we introduce in this paper a new Hilfer generalized proportional fractional derivative, which unifies the Riemann-Liouville and Caputo generalized proportional fractional derivative. Some important properties of the proposed derivative are presented. Based on the proposed derivative, we consider a nonlinear fractional differential equation with nonlocal initial condition and show that this equation is equivalent to the Volterra integral equation. In addition, the existence and uniqueness of solutions are proven using fixed point theorems. Furthermore, we offer two examples to clarify the results.
  • Article
    Citation - WoS: 6
    Citation - Scopus: 8
    On a Langevin Equation Involving Caputo Fractional Proportional Derivatives With Respect To Another Function
    (Amer inst Mathematical Sciences-aims, 2022) Jarad, Fahd; Laadjal, Zaid
    In this work, we introduce and study a class of Langevin equation with nonlocal boundary conditions governed by a Caputo fractional order proportional derivatives of an unknown function with respect to another function. The qualitative results concerning the given problem are obtained with the aid of the lower regularized incomplete Gamma function and applying the standard fixed point theorems. In order to homologate the theoretical results we obtained, we present two examples.