WoS İndeksli Yayınlar Koleksiyonu

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

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Publisher: search.filters.publisher.MdpiSubject: search.filters.subject.Fractional Derivatives

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  • Article
    Citation - WoS: 74
    Citation - Scopus: 86
    Analysis of Homotopy Perturbation Method for Solving Fractional Order Differential Equations
    (Mdpi, 2019) Baleanu, Dumitru; Waheed, Asif; Khan, Mansoor Shaukat; Affan, Hira; Javeed, Shumaila
    The analysis of Homotopy PerturbationMethod (HPM) for the solution of fractional partial differential equations (FPDEs) is presented. A unified convergence theorem is given. In order to validate the theory, the solution of fractional-order Burger-Poisson (FBP) equation is obtained. Furthermore, this work presents the method to find the solution of FPDEs, while the same partial differential equation (PDE) with ordinary derivative i.e., for alpha = 1, is not defined in the given domain. Moreover, HPM is applied to a complicated obstacle boundary value problem (BVP) of fractional order.
  • Article
    Citation - WoS: 44
    Citation - Scopus: 53
    Some New Fractional-Calculus Connections Between Mittag-Leffler Functions
    (Mdpi, 2019) Fernandez, Arran; Baleanu, Dumitru; Srivastava, Hari M.
    We consider the well-known Mittag-Leffler functions of one, two and three parameters, and establish some new connections between them using fractional calculus. In particular, we express the three-parameter Mittag-Leffler function as a fractional derivative of the two-parameter Mittag-Leffler function, which is in turn a fractional integral of the one-parameter Mittag-Leffler function. Hence, we derive an integral expression for the three-parameter one in terms of the one-parameter one. We discuss the importance and applications of all three Mittag-Leffler functions, with a view to potential applications of our results in making certain types of experimental data much easier to analyse.