WoS İndeksli Yayınlar Koleksiyonu

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

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Publisher: search.filters.publisher.Eudoxus Press, LlcSubject: search.filters.subject.Boundary Value Problem

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  • Article
    Citation - WoS: 6
    Citation - Scopus: 6
    A Caputo Fractional Order Boundary Value Problem With Integral Boundary Conditions
    (Eudoxus Press, Llc, 2013) Babakhani, Azizollah; Abdeljawad, Thabet; Abdeljawad, Thabet; Matematik
    In this paper, we discuss existence and uniqueness of solutions to nonlinear fractional order ordinary differential equations with integral boundary conditions in an ordered Banach space. We use the Caputo fractional differential operator and the nonlinearity depends on the fractional derivative of an unknown function. The nonlinear alternative of the Leray- Schauder type Theorem is the main tool used here to establish the existence and the Banach contraction principle to show the uniqueness of the solution under certain conditions. The compactness of solutions set is also investigated and an example is included to show the applicability of our results.
  • Article
    Citation - WoS: 5
    Citation - Scopus: 5
    Mild and Strong Solutions for a Fractional Nonlinear Neumann Boundary Value Problem
    (Eudoxus Press, Llc, 2013) Herzallah, Mohamed A. E.; Baleanu, Dumitru; El-Shahed, Moustafa; Baleanu, Dumitru; Matematik
    In this paper, we investigated the following fractional Neumann boundary value problem D-C(0)alpha+u(t) - lambda u(t) = f (t, u(t)), u'(0) = u'(1) = 0, 1 < alpha < 2, lambda not equal 0, where D-C(a+)alpha is the fractional Caputo derivative. We proved the existence of at least one mild solution and we determined when this solution is unique for suitable assumptions on the function f