Scopus İndeksli Yayınlar Koleksiyonu

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

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  • Article
    A Left-Definite Non-Integer-Order Dissipative Operator
    (Springer Nature, 2026) Ugurlu, Ekin
    In this paper we consider a non-integer (fractional)-order nonselfadjoint boundary-value problem so that the fractional-order equation is a kind of left-definite equation. We construct a dissipative operator in a Sobolev space H-1(a,b) and we introduce several results on the spectral properties of the related operators. In particular, we construct an inverse operator with the aid of the Dirac-delta function and we apply Krein's theorem to the inverse operator which is compact having a nuclear imaginary component.
  • Editorial
    Preface
    (Springer Nature, 2022) Agarwal, Ravi P.; Karapınar, Erdal; Burcu Özdemir Sarı, Ö.; Caner, Alp; Chen, Yangquan; Gazi, Orhan; Mahmoud, Khaled; Salim, Abdelkrim; Gülkan, Polat; Machado, José António Tenreiro; Kumar, Devendra; Lazreg, Jamal Eddine; Dutta, Hemen; Özdemir, Suna S.; Hristov, Jordan; Momani, Shaher; Purohit, Sunil Dutt; Anastassiou, George A.; Uzun, Nil; Baleanu, Dumitru; Benchohra, Mouffak; Singh, Jagdev; Cattani, Carlo; Agarwal, Praveen
  • Book Part
    Citation - Scopus: 8
    Advanced Topics in Fractional Differential Equations a Fixed Point Approach
    (Springer Nature, 2023) Benchohra, M.; Karapınar, Erdal; Karapınar, E.; Lazreg, J.E.; Salim, A.; Matematik
  • Editorial
    Preface
    (Springer Nature, 2023) Benchohra, M.; Karapinar, E.; Lazreg, J.E.; Salim, A.; Hristov, Jordan; Anastassiou, George A.; Baleanu, Dumitru; Singh, Jagdev; Cattani, Carlo; Kumar, Devendra; Dutta, Hemen; Matematik
  • Article
    Phenomenological Study of Lithium-Sodium Tetragermanate Close to the Phase Transition
    (Springer Nature, 2025) Kiraci, Ali
    This study presents an analysis of the dielectric and thermal properties in the vicinity of the second-order ferroelectric phase transition, with a specific emphasis on lithium-sodium tetragermanate, LiNaGe<inf>4</inf>O<inf>9</inf>. The power-law equation is employed by modifying the Kouvel-Fisher (KF) technique, which articulates the magnetization () and magnetic susceptibility in relation to the spontaneous polarization () and the dielectric constant () within ferroelectric frameworks. A parallel methodology is adopted to elucidate the heat capacity () and thermal expansivity () in the vicinity of phase transitions occurring in LiNaGe<inf>4</inf>O<inf>9</inf>. We demonstrate that the continuous fluctuations in and with temperature nearing the Curie point (T<inf>C</inf>108 K) as an indication of a second-order transition in LiNaGe<inf>4</inf>O<inf>9</inf>. Furthermore, a linear correlation is also established between and with temperature approaching the Curie point T<inf>C</inf> for this crystal structure. Experimental data are used from the literature for our analysis. Our findings show that the critical behavior of one dielectric or thermal property near the transition temperature in LiNaGe<inf>4</inf>O<inf>9</inf> can be predicted from the other through these linear relationships. The methodology articulated herein for delineating the dielectric and thermal characteristics of LiNaGe<inf>4</inf>O<inf>9</inf> close to the Curie point is extendable to various other ferroelectric materials. © 2025 Elsevier B.V., All rights reserved.
  • Book Part
    Introduction
    (Springer Nature, 2022) Karapınar, Erdal; Agarwal, Ravi P.
    Fixed point theory can be described as a framework for researching and investigating the existence of the solution of the equation f(p) = p for a certain self-mapping f that is defined on a non-empty set X. As is expected, here, p is called the fixed point of the mapping f. On the other side, we may re-consider the fixed point equation f(p) = p as T(p) = f(p) - p= 0 and, accordingly, finding the zeros of the mapping T and finding the fixed point of f becomes an equivalent statement. This equivalence, not only enriches the fixed point theory but also, opens the doors to a wide range of potential applications in the setting of almost all quantitative sciences. For example, let us consider one of the classical open problems of number theory, finding perfect numbers: Let p be a self-mapping on a natural number such that p(n) is the sum of all divisors of n for n&gt; 1. Thus, any fixed points of the function p give a perfect number. In particular, 6 is the smallest perfect numbers, and 2 74207280× (2 74207281- 1 ), with 44, 677, 235 digits, is the biggest known perfect number. © 2022 Elsevier B.V., All rights reserved.
  • Book Part
    Preliminary Background
    (Springer Nature, 2023) Benchohra, M.; Karapınar, E.; Lazreg, J.E.; Salim, A.
    In this chapter, we discuss the necessary mathematical tools, notations, and concepts we need in the succeeding chapters. We look at some essential properties of fractional differential operators. We also review some of the basic properties of measures of noncompactness and fixed point theorems which are crucial in our results regarding fractional differential equations. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
  • Book Part
    Introduction
    (Springer Nature, 2023) Benchohra, M.; Karapınar, E.; Lazreg, J.E.; Salim, A.
    Fractional calculus is a field in mathematical analysis which is a generalization of integer differential calculus that involves real or complex order derivatives and integrals [10–14, 25, 28, 43, 50–52]. There is a long history of this concept of fractional differential calculus. One might wonder what meaning could be attributed to the derivative of a fractional order, that is dnydxn, where n is a fraction. Indeed, in correspondence with Leibniz, L’Hopital considered this very possibility. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
  • Book Part
    Citation - Scopus: 15
    Fixed Point Theory in Generalized Metric Spaces
    (Springer Nature, 2022) Karapınar, E.; Agarwal, R.P.
  • Book Part
    Introduction
    (Springer Nature, 2023) Benchohra, M.; Karapınar, E.; Lazreg, J.E.; Salim, A.
    Fractional calculus is an area of mathematical analysis that extends the concepts of integer differential calculus to involve real or complex order derivatives and integrals. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.