Scopus İndeksli Yayınlar Koleksiyonu

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

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Now showing 1 - 10 of 27
  • Article
    Widths and Entropy of Sets of Smooth Functions on Compact Homogeneous Manifolds
    (Tubitak, 2021) LEVESLEY, Jeremy; KUSHPEL, Alexander; Taş, Kenan
    We develop a general method to calculate entropy and n-widths of sets of smooth functions on an arbitrary compact homogeneous Riemannian manifold Md . Our method is essentially based on a detailed study of geometric characteristics of norms induced by subspaces of harmonics on Md . This approach has been developed in the cycle of works [1, 2, 10–19]. The method’s possibilities are not confined to the statements proved but can be applied in studying more general problems. As an application, we establish sharp orders of entropy and n-widths of Sobolev’s classes Wγ p ( Md ) and their generalisations in Lq ( Md ) for any 1 < p, q < ∞. In the case p, q = 1, ∞ sharp in the power scale estimates are presented.
  • Article
    A Behavioral Perspective on Price Convergence via Perturbed Metric Spaces with an Extended Contraction
    (Association of Mathematicians (MATDER), 2026) Bilazeroğlu, Şeyma
    In this study, we examine how investors update their price forecasts over time within a "perturbated metric space," which incorporates behavioral influences and market friction. Classical metric structures are inadequate when the measured distance changes with perceived deviations. Therefore, a new structure is proposed in which the measured distance is modified by perceived deviations. In this context, the existence of a fixed point is guaranteed through an extended contraction inequality, and the convergence behavior of the model is analyzed using different examples. Simulations established under different linear and nonlinear update functions demonstrate that the model can reflect both slow and fast market behaviors that reach equilibrium. The proposed approach mathematically demonstrates that investors can reach a common price expectation in the long run, even with heterogeneous psychological responses.
  • Article
    Citation - Scopus: 25
    On the Geometric and Physical Properties of Conformable Derivative
    (Murat TOSUN, 2024) Has, A.; Yılmaz, B.; Baleanu, D.
    In this article, we explore the advantages geometric and physical implications of the conformable derivative. One of the key benefits of the conformable derivative is its ability to approximate the tangent at points where the classical tangent is not readily available. By employing conformable derivatives, alternative tangents can be created to overcome this limitation. Thanks to these alternative (conformable) tangents, physical interpretation can be made with alternative velocity vectors. Furthermore, the conformable derivative proves to be valuable in situations where the tangent plane cannot be defined. It enables the creation of alternative tangent planes, offering a solution in cases where the traditional approach falls short. Geometrically speaking, the conformable derivative carries significant meaning. It provides insights into the local behavior of a function and its relationship with nearby points. By understanding the conformable derivative, we gain a deeper understanding of how a function evolves and changes within its domain. A several examples are presented in the article to better understand the article and visualize the concepts discussed. These examples are accompanied by visual representations generated using the Mathematica program, aiding in a clearer understanding of the proposed ideas. By combining theoretical explanations, practical examples, and visualizations, this article aims to provide a comprehensive exploration of the advantages and geometric and physical implications of the conformable derivative. © MSAEN.
  • Article
    On Solutions of Variable-Order Fractional Differential Equations
    (Elsevier B.V., 2017) Akgül, Ali; Inc, Mustafa; Baleanu, Dumitru; Abdalla, Bahaaeldin; Jarad, Fahd; Bouchelaghem, Faycal; Abdeljawad, Thabet; Ardjouni, Abdelouaheb; Boulares, Hamid; Shah, Kamal
    Numerical calculation of the fractional integrals and derivatives is the code tosearch fractional calculus and solve fractional differential equations. The exactsolutions to fractional differential equations are compelling to get in real ap-plications, due to the nonlocality and complexity of the fractional differentialoperators, especially for variable-order fractional differential equations. There-fore, it is significant to enhance numerical methods for fractional differentialequations. In this work, we consider variable-order fractional differential equa-tions by reproducing kernel method. There has been much attention in theuse of reproducing kernels for the solutions to many problems in the recentyears. We give an example to demonstrate how efficiently our theory can beimplemented in practice.
  • 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 - WoS: 3
    Citation - Scopus: 3
    The Lebesgue Constants on Projective Spaces
    (Tubitak, 2021) Kushpel, Alexander
    We give the solution of a classical problem of Approximation Theory on sharp asymptotic of the Lebesgueconstants or norms of the Fourier-Laplace projections on the real projective spaces Pd(R). In particular, these resultsextend sharp asymptotic found by Fejer [2] in the case of S1in 1910 and by Gronwall [4] in 1914 in the case of S2. Thecase of spheres, Sd, complex and quaternionic projective spaces, Pd(C), Pd(H) and the Cayley elliptic plane P16(Cay)was considered by Kushpel [8].
  • 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.