WoS İndeksli Yayınlar Koleksiyonu

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

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Publisher: search.filters.publisher.Pergamon-Elsevier Science LtdSubject: 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.