Scopus İndeksli Yayınlar Koleksiyonu

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

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Author: search.filters.author.Jarad, FahdPublisher: search.filters.publisher.Univ Nis, Fac Sci Math

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Now showing 1 - 4 of 4
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    On the Quantitative Weighted Generalization of Jafari Transform
    (Univ Nis, Fac Sci Math, 2025) Yazici, Serdal; Cekim, Bayram; Jarad, Fahd; Jafari, Hossein
    In this paper, a quantitative weighted transform based on the Jafari transform is proposed, and the mathematical foundations of this new transform are investigated. In the first section, some information about Jafari transform and some mathematical tools are reviewed. In the second section, the quantitative weighted Jafari transform is introduced, its existence guaranteed through a theorem, and its fundamental properties are examined. Additionally, transforms of the fractional derivative and fractional integral of a function with respect to a function h and a w-weight are obtained. In the third section, the theoretical findings are applied to solve classical and fractional initial value problems based on a function h and w-weight. In the last section, the results are discussed.
  • 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
    Citation - WoS: 45
    Citation - Scopus: 51
    Ulam Stability for Delay Fractional Differential Equations With a Generalized Caputo Derivative
    (Univ Nis, Fac Sci Math, 2018) Abdeljawad, Thabet; Ameen, Raad; Jarad, Fahd
    The objective of this paper is to extend Ulam-Hyers stability and Ulam-Hyers-Rassias stability theory to differential equations with delay and in the frame of a certain class of a generalized Caputo fractional derivative with dependence on a kernel function. We discuss the conditions such delay generalized Caputo fractional differential equations should satisfy to be stable in the sense of Ulam-Hyers and Ulam-Hyers-Rassias. To demonstrate our results two examples are presented.
  • Article
    Citation - WoS: 63
    Citation - Scopus: 74
    On Generalized Fractional Operators and a Gronwall Type Inequality With Applications
    (Univ Nis, Fac Sci Math, 2017) Abdeljawad, Thabet; Adjabi, Yassine; Jarad, Fahd
    In this paper, we obtain the Gronwall type inequality for generalized fractional operators unifying Riemann-Liouville and Hadamard fractional operators. We apply this inequality to the dependence of the solution of differential equations, involving generalized fractional derivatives, on both the order and the initial conditions. More properties for the generalized fractional operators are formulated and the solutions of initial value problems in certain new weighted spaces of functions are established as well.