WoS İndeksli Yayınlar Koleksiyonu

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

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Institution Author: search.filters.institutionAuthor.Ugurlu, EkinSubject: search.filters.subject.Fractional Derivatives

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  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    Left-Definite Fractional Hamiltonian Systems: Titchmarsh-Weyl Theory
    (Pergamon-Elsevier Science Ltd, 2025) Ugurlu, Ekin
    Hamiltonian systems are useful when formally symmetric boundary value problems generated by ordinary derivatives are considered. However, if the ordinary derivatives are changed by non-integer-order (fractional) derivatives, it is not easy to investigate the corresponding problems. In this paper, we introduce a systematic approach to dealing with fractional boundary value problems by constructing a fractional Hamiltonian system. In particular, we consider a left-definite system, and we construct nested-circles theory (Weyl theory) for this system of equations. Using the Titchmarsh-Weyl function, we prove that at least r-solutions of the 2r-dimensional system of equations should be Dirichlet-integrable on a given interval.
  • Article
    Citation - WoS: 5
    Citation - Scopus: 5
    On Some Fractional Operators Generated From Abel's Formula
    (Tubitak Scientific & Technological Research Council Turkey, 2022) Ugurlu, Ekin
    This work aims to share some fractional integrals and derivatives containing three real parameters. The main tool to introduce such operators is the corresponding Abel's equation. Solvability conditions for the Abel's equations are shared. Semigroup property for fractional integrals are introduced. Integration by parts rule is given. Moreover, mean value theorems and related results are shared. At the end of the paper, some directions for some fractional operators are given.