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 22
  • Article
    Citation - Scopus: 1
    Study of Impulsive Problem with Caputo Fractional Derivative Involving Nonlocal Conditions Using Fixed Point Theory
    (Kyungnam University Press, 2025) Dhandapani, Swathi; Umapathi, Karthik Raja; Mathuraiveeran, Jeyaraman; Shah, Kamal; Abdeljawad (Maraaba) T., Thabet; Jarad, Fahd; Abdeljawad, Thabet
    In this article, we study the existence of solutions for an impulsive Caupto fractional differential equations with a class of initial value problem dependence on the Lipschitz first derivative conditions. Our main tool is a Banach's fixed point theorem and Leray-Schauder fixed point theorem. We also investigate the existence of fractional Derivative with non-local conditions. An numerical example is given to clarify the results. © 2025 Elsevier B.V., All rights reserved.
  • Article
    Citation - WoS: 4
    Citation - Scopus: 4
    Fractional Vector Calculus in the Frame of a Generalized Caputo Fractional Derivative
    (Univ Politehnica Bucharest, Sci Bull, 2018) Jarad, Fahd; Gambo, Yusuf Ya'u; Baleanu, Dumitru; Jarad, Fahd; Baleanu, Dumitru; Abdeljawad, Thabet; Abdeljawad, Thabet; Matematik
    The authors in [1] recently introduced a new generalized fractional derivative on AC(y)(n)[a ,b] and C-y(n)[a, b], and defined their Caputo version. This derivative contains two parameters and reduces to the classical Caputo derivatives if one of these parameters tend to certain values. From here and after, by generalized Caputo fractional derivative, we refer to the Caputo version of the generalized fractional derivative. This paper studies the generalized Caputo fractional derivative and establishes the Fundamental Theorem of Fractional Calculus (FTFC) in the sense of this derivative. The fundamental results are used in establishing some vital theorems and then applied to vector calculus.
  • Article
    Citation - WoS: 60
    Citation - Scopus: 68
    Lyapunov-Krasovskii Stability Theorem for Fractional Systems With Delay
    (Editura Acad Romane, 2011) Baleanu, Dumitru; Baleanu, D.; Ranjbar N, A.; Abdeljawad, Thabet; Sadati R, S. J.; Delavari, R. H.; Abdeljawad (Maraaba), T.; Gejji, V.; Matematik
    Fractional calculus techniques and methods started to be applied during the last decades in several fields of science and engineering. In this paper we studied the stability of fractional order nonlinear time-delay systems for Caputo's derivative and we extended Lyapunov-Krasovskii theorem for the fractional nonlinear systems.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 5
    Some Fixed Point Results in Tvs-Cone Metric Spaces
    (House Book Science-casa Cartii Stiinta, 2013) Abdeljawad, T.; Abdeljawad, Thabet; Rezapour, Sh; Matematik
    Every TVS-cone metric space is topologically isomorphic to a topological metric space. In this paper, by using a nonlinear scalarization, we give some fixed point results with nonlinear contractive conditions on TVS-cone metric spaces.
  • Article
    Citation - WoS: 7
    Citation - Scopus: 6
    Perron's Theorem for Q-Delay Difference Equations
    (Natural Sciences Publishing Corp-nsp, 2011) Alzabut, Jehad; Alzabut, J. O.; Abdeljawad, T.; Abdeljawad, Thabet; Matematik
    In this paper, we prove that if a linear q-delay difference equation satisfies Perron's condition then its trivial solution is uniformly asymptotically stable.
  • Article
    Citation - WoS: 3
    Citation - Scopus: 3
    The Property of Smallness Up To a Complemented Banach Subspace
    (Kossuth Lajos Tudomanyegyetem, 2004) Abdeljawad, T; Abdeljawad, Thabet; Yurdakul, M; Matematik
    This article investigates locally convex spaces which satisfy the property of smallness up to a complemented Banach subspace, the SCBS property, which was introduced by Djakov, Terzioglu, Yurdakul and Zahariuta. It is proved that a bounded perturbation of an automorphism on a complete barrelled locally convex, space with the SCBS is stable up to a Banach subspace. New examples are given, and the relation of the SCBS with the quasinormability is analyzed. It is proved that the Frechet space l(p+) does not satisfy the SCBS, therefore this property is not inherited by subspaces or separated quotients.
  • Article
    Citation - WoS: 16
    Citation - Scopus: 16
    A Gap in the Paper "a Note on Cone Metric Fixed Point Theory and Its Equivalence" [Nonlinear Anal. 72(5), (2010), 2259-2261]
    (Gazi Univ, 2011) Abdeljawad, Thabet; Karapinar, Erdal
    There is a gap in Theorem 2.2 of the paper of Du [1]. In this paper, we shall state the gap and repair it.
  • Article
    Citation - WoS: 1
    Citation - Scopus: 2
    Some Results for Two Classes of Two-Point Local Fractional Proportional Boundary Value Problems
    (Univ Nis, Fac Sci Math, 2023) Jarad, Fahd; Laadjal, Zaid; Abdeljawad, Thabet
    In this paper, we consider two classes of boundary value problems in the frame of local proportional fractional derivatives. For both of these classes, we obtain the associated Green's functions and discuss their properties. Using these properties, we go about the uniqueness of the solutions. In addition, we establish Lyapunov-type and Hartman-Wintner-type inequalities and build sharp estimated for the unique solutions of the considered equations.
  • Article
    Edelstein-Type Fixed Point Theorems in Compact Tvs-Cone Metric Spaces
    (Hacettepe University, 2014) Abdeljawad, Thabet
    In this paper we prove two fixed point theorems in compact cone metricspaces over normal cones. The first theorem generalizes Edelstein theorem [8] and is different from the generalization obtained in [11]. Thesecond theorem generalizes the main result in [10] and the first theorem.However, the two theorems fail in different categories. Moreover, different versions of the two theorems are proved in TVS-cone metric spacesby making use of the nonlinear scalarization function used very recentlyby Wei-Shih Du in [A note on cone metric fixed point theory and itsequivalence, Nonlinear Analysis,72(5),2259-2261 (2010).] to prove theequivalence of the Banach contraction principle in cone metric spacesand usual metric spaces.
  • Article
    Common fixed point theorems in cone Banach spaces
    (Hacettepe Univ, FAC Sci, 2011) Abdeljawad, Thabet; Karapınar, Erdal; Taş, Kenan; Tas, Aysegul; Kumar, Anil
    Recently, E. Karapınar (Fixed Point Theorems in Cone Banach Spaces, Fixed Point Theory Applications, Article ID 609281, 9 pages, 2009) presented some fixed point theorems for self-mappings satisfying certain contraction principles on a cone Banach space. Here we will give some generalizations of this theorem.