WoS İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653

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Department: search.filters.department.Çankaya UniversitySubject: search.filters.subject.Generalized Caputo Fractional Derivatives

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Now showing 1 - 3 of 3
  • Article
    Citation - WoS: 12
    Citation - Scopus: 15
    Variational Principles in the Frame of Certain Generalized Fractional Derivatives
    (Amer inst Mathematical Sciences-aims, 2020) Jarad, Fahd; Abdeljawad, Thabet
    In this article, we study generalized fractional derivatives that contain kernels depending on a function on the space of absolute continuous functions. We generalize the Laplace transform in order to be applicable for the generalized fractional integrals and derivatives and apply this transform to solve some ordinary differential equations in the frame of the fractional derivatives under discussion.
  • 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: 261
    On the Generalized Fractional Derivatives and Their Caputo Modification
    (int Scientific Research Publications, 2017) Jarad, Fahd; Abdeljawad, Thabet; Baleanu, Dumitru
    In this manuscript, we define the generalized fractional derivative on AC(gamma)(n) [a, b], the space of functions defined on [a, b] such that gamma(n-1) f is an element of AC [a, b], where gamma = x(1-rho) d/dx. We present some of the properties of generalized fractional derivatives of these functions and then we define their Caputo version. (C) 2017 All rights reserved.