Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 1Citation - Scopus: 1Left-Definite Fractional Hamiltonian Systems: Titchmarsh-Weyl Theory(Pergamon-Elsevier Science Ltd, 2025) Ugurlu, EkinHamiltonian 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: 2Citation - Scopus: 2Fractional Hamiltonian Systems: Nested Ellipsoids(Pergamon-elsevier Science Ltd, 2025) Ugurlu, EkinIn this paper, we introduce a singular fractional-order Hamiltonian system with several spectral parameters. Using the inertia indices of the corresponding Hermitian forms we provide a lower bound for the number of linearly independent integrable-square solutions. Moreover, we introduce the Titchmarsh-Weyl function together with an intermediate theorem on the number of the integrable-square solutions. At the end of the paper, we show that 2-sequential and 4-sequential scalar fractional-order differential equations can be embedded into such Hamiltonian systems.Article Citation - WoS: 6Citation - Scopus: 6On Square Integrable Solutions of a Fractional Differential Equation(Elsevier Science inc, 2018) Ugurlu, Ekin; Baleanu, Dumitru; Tas, KenanIn this paper we construct the Weyl-Titchmarsh theory for the fractional Sturm-Liouville equation. For this purpose we used the Caputo and Riemann-Liouville fractional operators having the order is between zero and one. (C) 2018 Elsevier Inc. All rights reserved.