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 23
  • Article
    Citation - WoS: 5
    Citation - Scopus: 5
    On Some Fractional Operators Generated From Abel's Formula
    (Tubitak Scientific & Technological Research Council Turkey, 2022) Ugurlu, Ekin
    This work aims to share some fractional integrals and derivatives containing three real parameters. The main tool to introduce such operators is the corresponding Abel's equation. Solvability conditions for the Abel's equations are shared. Semigroup property for fractional integrals are introduced. Integration by parts rule is given. Moreover, mean value theorems and related results are shared. At the end of the paper, some directions for some fractional operators are given.
  • Article
    Citation - WoS: 6
    The Complementary Nabla Bennett-Leindler Type Inequalities
    (Ankara Univ, Fac Sci, 2022) Kayar, Zeynep; Kaymakcalan, Billur
    We aim to find the complements of the Bennett-Leindler type inequalities in nabla time scale calculus by changing the exponent from 0 < zeta < 1 to zeta > 1. Different from the literature, the directions of the new inequalities, where zeta > 1, are the same as that of the previous nabla Bennett-Leindler type inequalities obtained for 0 < zeta < 1. By these settings, we not only complement existing nabla Bennett-Leindler type inequalities but also generalize them by involving more exponents. The dual results for the delta approach and the special cases for the discrete and continuous ones are obtained as well. Some of our results are novel even in the special cases.
  • Conference Object
    Citation - WoS: 1
    Strengthening of Columns With Different Innovative Composite Materials for Rc Buildings Without Sufficient Earthquake Resistance
    (Gazi Univ, 2022) Mercimek, Omer; Ghoroubi, Rahim; Ozdemir, Anil; Anil, Ozgur
    The Turkey includes the world's second most active faults and is geographically situated at a very high seismic activity. Research on strengthening RC (reinforced-concrete) structures without adequate earthquake resistance has become an extremely important issue. Taking into account the objectives of this research, an experimental study is designed to strengthen the columns without adequate earthquake resistance by using carbon-reinforced-fiber-fabric (CFRP) strips and textile-reinforced-mortar (TRM) layers with two separate types of advanced composite materials. The variables evaluated within the study horizon are the composite material type used for strengthening, the width of the strip, and whether or not the anchor is used at the point of strip overlap. In this experiment, nine RC column were produced and were tested by affecting axial load, which are the reference test specimens without strengthening and eight RC column test specimens strengthened with two separate types of composite material. The loaddisplacement behavior, initial stiffness value, energy dissipation capacities, ultimate load capacity and displacement ductility ratios have been measured according to the test results. It was also examined which of the two different composite materials used to strengthen the columns of the RC is more efficient in improving the columns performance.
  • Article
    Citation - WoS: 13
    Citation - Scopus: 15
    Hardy-Copson Type Inequalities for Nabla Time Scale Calculus
    (Tubitak Scientific & Technological Research Council Turkey, 2021) Kaymakcalan, Billur; Kayar, Zeynep
    This paper is devoted to the nabla unification of the discrete and continuous Hardy?Copson type inequalities. Some of the obtained inequalities are nabla counterparts of their delta versions while the others are new even for the discrete, continuous, and delta cases. Moreover, these dynamic inequalities not only generalize and unify the related ones in the literature but also improve them in the special cases.
  • Article
    Citation - Scopus: 20
    Evolutionary Mathematical Science, Fractional Modeling and Artificial Intelligence of Nonlinear Dynamics in Complex Systems
    (Akif AKGUL, 2022) Karaca, Yeliz; Baleanu, Dumitru
    Complex problems in nonlinear dynamics foreground the critical support of artificial phenomena so that each domain of complex systems can generate applicable answers and solutions to the pressing challenges. This sort of view is capable of serving the needs of different aspects of complexity by minimizing the problems of complexity whose solutions are based on advanced mathematical foundations and analogous algorithmic models consisting of numerous applied aspects of complexity. Evolutionary processes, nonlinearity and all the other dimensions of complexity lie at the pedestal of time, reveal time and occur within time. In the ever-evolving landscape and variations, with causality breaking down, the idea of complexity can be stated to be a part of unifying and revolutionary scientific framework to expound complex systems whose behavior is perplexing to predict and control with the ultimate goal of attaining a global understanding related to many branches of possible states as well as high-dimensional manifolds, while at the same time keeping abreast with actuality along the evolutionary and historical path, which itself, has also been through different critical points on the manifold. In view of these, we put forth the features of complexity of varying phenomena, properties of evolution and adaptation, memory effects, nonlinear dynamic system qualities, the importance of chaos theory and applications of related aspects in this study. In addition, processes of fractional dynamics, differentiation and systems in complex systems as well as the dynamical processes and dynamical systems of fractional order with respect to natural and artificial phenomena are discussed in terms of their mathematical modeling. Fractional calculus and fractional-order calculus approach to provide novel models with fractional-order calculus as employed in machine learning algorithms to be able to attain optimized solutions are also set forth besides the justification of the need to develop analytical and numerical methods. Subsequently, algorithmic complexity and its goal towards ensuring a more effective handling of efficient algorithms in computational sciences is stated with regard to the classification of computational problems. We further point out the neural networks, as descriptive models, for providing the means to gather, store and use experiential knowledge as well as Artificial Neural Networks (ANNs) in relation to their employment for handling experimental data in different complex domains. Furthermore, the importance of generating applicable solutions to problems for various engineering areas, medicine, biology, mathematical science, applied disciplines and data science, among many others, is discussed in detail along with an emphasis on power of predictability, relying on mathematical sciences, with Artificial Intelligence (AI) and machine learning being at the pedestal and intersection with different fields which are characterized by complex, chaotic, nonlinear, dynamic and transient components to validate the significance of optimized approaches both in real systems and in related realms.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 6
    Diamond Alpha Hardy-Copson Type Dynamic Inequalities
    (Hacettepe Univ, Fac Sci, 2022) Kaymakcalan, Billur; Kayar, Zeynep
    In this paper two kinds of dynamic Hardy-Copson type inequalities are derived via diamond alpha integrals. The first kind consists of twelve new integral inequalities which can be considered as mixed type in the sense that these inequalities contain delta, nabla and diamond alpha integrals together. The second kind involves another twelve new inequalities, which are composed of only diamond alpha integrals, unifying delta and nabla Hardy-Copson type inequalities. Our approach is quite new due to the fact that it uses time scale calculus rather than algebra. Therefore both kinds of our results unify some of the known delta and nabla Hardy-Copson type inequalities into one diamond alpha Hardy-Copson type inequalities and offer new Hardy-Copson type inequalities even for the special cases.
  • Article
    Citation - WoS: 3
    Citation - Scopus: 3
    Left-Definite Hamiltonian Systems and Corresponding Nested Circles
    (Tubitak Scientific & Technological Research Council Turkey, 2023) Ugurlu, Ekin
    This work aims to construct the Titchmarsh-Weyl M(A)-theory for an even-dimensional left-definite Hamiltonian system. For this purpose, we introduce a suitable Lagrange formula and selfadjoint boundary conditions including the spectral parameter A. Then we obtain circle equations having nesting properties. Using the intersection point belonging to all the circles we share a lower bound for the number of Dirichlet-integrable solutions of the system.
  • Article
    Citation - Scopus: 27
    A Caputo-Fabrizio Fractional-Order Cholera Model and Its Sensitivity Analysis
    (Mehmet Yavuz, 2023) Akgül, A.; Jarad, F.; Kumam, P.; Nonlaopon, K.; Ahmed, I.
    In recent years, the availability of advanced computational techniques has led to a growing emphasis on fractional-order derivatives. This development has enabled researchers to explore the intricate dynamics of various biological models by employing fractional-order derivatives instead of traditional integer-order derivatives. This paper proposes a Caputo-Fabrizio fractional-order cholera epidemic model. Fixed-point theorems are utilized to investigate the existence and uniqueness of solutions. A recent and effective numerical scheme is employed to demonstrate the model’s complex behaviors and highlight the advantages of fractional-order derivatives. Additionally, a sensitivity analysis is conducted to identify the most influential parameters. © 2023 by the authors.
  • Article
    Citation - WoS: 1
    Scattering and Characteristic Functions of a Dissipative Operator Generated by a System of Equations
    (Tubitak Scientific & Technological Research Council Turkey, 2021) Ugurlu, Ekin; Bayram, Elgiz; Tas, Kenan
    In this paper, we consider a system of first-order equations with the same eigenvalue parameter together with dissipative boundary conditions. Applying Lax-Phillips scattering theory and Sz.-Nagy-Foias model operator theory we prove a completeness theorem.
  • Article
    On a Fifth-Order Nonselfadjoint Boundary Value Problem
    (Tubitak Scientific & Technological Research Council Turkey, 2021) Ugurlu, Ekin; Tas, Kenan
    In this paper we aim to share a way to impose some nonselfadjoint boundary conditions for the solutions of a formally symmetric fifth-order differential equation. Constructing a dissipative operator related with the problem we obtain some informations on spectral properties of the problem. In particular, using coordinate-free approach we construct characteristic matrix-function related with the contraction which is obtained with the aid of the dissipative operator. In this paper we aim to share a way to impose some nonselfadjoint boundary conditions for the solutions of a formally symmetric fifth-order differential equation. Constructing a dissipative operator related with the problem we obtain some informations on spectral properties of the problem. In particular, using coordinate-free approach we construct characteristic matrix-function related with the contraction which is obtained with the aid of the dissipative