Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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Now showing 1 - 10 of 24
  • Article
    Citation - WoS: 6
    Citation - Scopus: 20
    Discussions on Proinov-Cb Mapping on B-Metric Space
    (Wiley, 2023) Fulga, Andreea; Karapinar, Erdal
    In the present paper, we introduce the notion of Proinov-C-b-contraction mapping and we discuss it within the most interesting abstract structure, namely, b-metric spaces. We further take into consideration the necessary conditions to guarantee the existence and uniqueness of fixed points for such mappings, as well as indicate the validity of the main results by providing illustrative examples.
  • Article
    A New Iteration Scheme for Approximating Common Fixed Points in Uniformly Convex Banach Spaces
    (Wiley, 2023) Agwu, Imo Kalu; Ishtiaq, Umar; Jarad, Fahd; Saleem, Naeem
    In this paper, firstly, we introduce a method for finding common fixed point of L-Lipschitzian and total asymptotically strictly pseudo-non-spreading self-mappings and L-Lipschitzian and total asymptotically strictly pseudo-non-spreading non-self-mappings in the setting of a real uniformly convex Banach space. Secondly, the demiclosedness principle for total asymptotically strictly pseudo-non-spreading non-self-mappings is established. Thirdly, the weak convergence theorems of the proposed method to the common fixed point of the above mappings are proved. Our results improved, extended, and generalized some corresponding results in the literature.
  • Article
    Citation - WoS: 14
    Citation - Scopus: 15
    Solving Integral Equations by Means of Fixed Point Theory
    (Wiley, 2022) Fulga, A.; Shahzad, N.; Roldan Lopez de Hierro, A. F.; Karapinar, E.
    One of the most interesting tasks in mathematics is, undoubtedly, to solve any kind of equations. Naturally, this problem has occupied the minds of mathematicians since the dawn of algebra. There are hundreds of techniques for solving many classes of equations, facing the problem of finding solutions and studying whether such solutions are unique or multiple. One of the recent methodologies that is having great success in this field of study is the fixed point theory. Its iterative procedures are applicable to a great variety of contexts in which other algorithms fail. In this paper, we study a very general class of integral equations by means of a novel family of contractions in the setting of metric spaces. The main advantage of this family is the fact that its general contractivity condition can be particularized in a wide range of ways, depending on many parameters. Furthermore, such a contractivity condition involves many distinct terms that can be either adding or multiplying between them. In addition to this, the main contractivity condition makes use of the self-composition of the operator, whose associated theorems used to be more general than the corresponding ones by only using such mapping. In this setting, we demonstrate some fixed point theorems that guarantee the existence and, in some cases, the uniqueness, of fixed points that can be interpreted as solutions of the mentioned integral equations.
  • Article
    Citation - WoS: 11
    Citation - Scopus: 12
    Results on Implicit Fractional Pantograph Equations With Mittag-Leffler Kernel and Nonlocal Condition
    (Wiley, 2022) Panchal, Satish K.; Jarad, Fahd; Almalahi, Mohammed A.
    In this study, the main focus is on an investigation of the sufficient conditions of existence and uniqueness of solution for two-classess of nonlinear implicit fractional pantograph equations with nonlocal conditions via Atangana-Baleanu-Riemann-Liouville (ABR) and Atangana-Baleanu-Caputo (ABC) fractional derivative with order sigma is an element of 1,2. We introduce the properties of solutions as well as stability results for the proposed problem without using the semigroup property. In the beginning, we convert the given problems into equivalent fractional integral equations. Then, by employing some fixed-point theorems such as Krasnoselskii and Banach's techniques, we examine the existence and uniqueness of solutions to proposed problems. Moreover, by using techniques of nonlinear functional analysis, we analyze Ulam-Hyers (UH) and generalized Ulam-Hyers (GUH) stability results. As an application, we provide some examples to illustrate the validity of our results.
  • Article
    Shape Preserving Piecewise Knr Fractional Order Biquadratic C<sup>2</Sup> Spline
    (Wiley, 2021) Riaz, Muhammad Bilal; Jarad, Fahd; Jasim, Hayder Natiq; Enver, Aytekin; Kirmani, Syed Khawar Nadeem
    In a recent article, a piecewise cubic fractional spline function is developed which produces C-1 continuity to given data points. In the present paper, an interpolant continuity class C-2 is preserved which gives visually pleasing piecewise curves. he behavior of the resulting representations is analyzed intrinsically with respect to variation of the shape control parameters t and s. The data points are restricted to be strictly monotonic along real line.
  • Article
    Citation - Scopus: 2
    Quadruple Best Proximity Points With Applications To Functional and Integral Equations
    (Wiley, 2022) Rashwan, Rashwan A.; Nafea, A.; Jarad, Fahd; Hammad, Hasanen A.
    This manuscript is devoted to obtaining a quadruple best proximity point for a cyclic contraction mapping in the setting of ordinary metric spaces. The validity of the theoretical results is also discussed in uniformly convex Banach spaces. Furthermore, some examples are given to strengthen our study. Also, under suitable conditions, some quadruple fixed point results are presented. Finally, as applications, the existence and uniqueness of a solution to a system of functional and integral equations are obtained to promote our paper.
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    The Extended Laguerre Polynomials {aq,n <sup>(a)</Sup>} (X) Involving Q<sup>f</Sup>q, Q &gt; 2
    (Wiley, 2022) Kalim, Muhammad; Akguel, Ali; Jarad, Fahd; Khan, Adnan; Akgül, Ali
    In this paper, for the proposed extended Laguerre polynomials {A(q,n )((alpha))}, the generalized hypergeometric function of the type (F)(q)(q), q > 2 and extension of the Laguerre polynomial are introduced. Similar to those related to the Laguerre polynomials, the generating function, recurrence relations, and Rodrigue's formula are determined. Some corollaries are also discussed at the end.
  • Article
    Citation - WoS: 7
    Citation - Scopus: 7
    On Extended B-Rectangular and Controlled Rectangular Fuzzy Metric-Like Spaces With Application
    (Wiley, 2022) Furqan, Salman; Jarad, Fahd; Saleem, Naeem
    In this article, we introduce the notions of extended b-rectangular and controlled rectangular fuzzy metric-like spaces that generalize many fuzzy metric spaces in the literature. We give examples to justify our newly defined fuzzy metric-like spaces and prove that these spaces are not Hausdorff. We use fuzzy contraction and prove Banach fixed point theorems in these spaces. As an application, we utilize our main results to solve the uniqueness of the solution of a differential equation occurring in the dynamic market equilibrium.
  • Article
    Citation - WoS: 4
    Citation - Scopus: 6
    On Atangana-Baleanu Nonlocal Boundary Fractional Differential Equations
    (Wiley, 2022) Almalahi, Mohammed A.; Panchal, Satish K.; Abdo, Mohammed S.; Jarad, Fahd
    This research paper is devoted to investigating two classes of boundary value problems for nonlinear Atangana-Baleanu-type fractional differential equations with Atangana-Baleanu fractional integral conditions. The applied fractional derivatives work as the nonlocal and nonsingular kernel. Upon using Krasnoselskii's and Banach's fixed point techniques, we establish the existence and uniqueness of solutions for proposed problems. Moreover, the Ulam-Hyers stability theory is constructed by using nonlinear analysis. Eventually, we provide two interesting examples to illustrate the effectiveness of our acquired results.
  • Article
    Citation - WoS: 52
    Citation - Scopus: 53
    Numerical Analysis of the Fractional-Order Nonlinear System of Volterra Integro-Differential Equations
    (Wiley, 2021) Ullah, Roman; Khan, Adnan; Shah, Rasool; Kafle, Jeevan; Mahariq, Ibrahim; Jarad, Fahd; Sunthrayuth, Pongsakorn
    This paper presents the nonlinear systems of Volterra-type fractional integro-differential equation solutions through a Chebyshev pseudospectral method. The proposed method is based on the Caputo fractional derivative. The results that we get show the accuracy and reliability of the present method. Different nonlinear systems have been solved; the solutions that we get are compared with other methods and the exact solution. Also, from the presented figures, it is easy to conclude that the CPM error converges quickly as compared to other methods. Comparing the exact solution and other techniques reveals that the Chebyshev pseudospectral method has a higher degree of accuracy and converges quickly towards the exact solution. Moreover, it is easy to implement the suggested method for solving fractional-order linear and nonlinear physical problems related to science and engineering.