Scopus İndeksli Yayınlar Koleksiyonu

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

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Institution Author: search.filters.institutionAuthor.Abdeljawad, ThabetWoS Q: search.filters.wosQuartile.Q1

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  • Article
    Citation - WoS: 1650
    Citation - Scopus: 1877
    On Conformable Fractional Calculus
    (Elsevier Science Bv, 2015) Abdeljawad, Thabet
    Recently, the authors Khalil et al. (2014) introduced a new simple well-behaved definition of the fractional derivative called conformable fractional derivative. In this article we proceed on to develop the definitions there and set the basic concepts in this new simple interesting fractional calculus. The fractional versions of chain rule, exponential functions, Gronwall's inequality, integration by parts, Taylor power series expansions, Laplace transforms and linear differential systems are proposed and discussed. (C) 2014 Elsevier By. All rights reserved.
  • Article
    Citation - WoS: 85
    Citation - Scopus: 101
    Dual Identities in Fractional Difference Calculus Within Riemann
    (Springeropen, 2013) Abdeljawad, Thabet
    We investigate two types of dual identities for Riemann fractional sums and differences. The first type relates nabla- and delta-type fractional sums and differences. The second type represented by the Q-operator relates left and right fractional sums and differences. These dual identities insist that in the definition of right fractional differences, we have to use both nabla and delta operators. The solution representation for a higher-order Riemann fractional difference equation is obtained as well.
  • Article
    Citation - WoS: 595
    Citation - Scopus: 680
    On Riemann and Caputo Fractional Differences
    (Pergamon-elsevier Science Ltd, 2011) Abdeljawad, Thabet
    In this paper, we define left and right Caputo fractional sums and differences, study some of their properties and then relate them to Riemann-Liouville ones studied before by Miller K. S. and Ross B., Atici F.M. and Eloe P. W., Abdeljawad T. and Baleanu D., and a few others. Also, the discrete version of the Q-operator is used to relate the left and right Caputo fractional differences. A Caputo fractional difference equation is solved. The solution proposes discrete versions of Mittag-Leffler functions. (C) 2011 Elsevier Ltd. All rights reserved.