Two-point boundary value problems for the generalized Bagley-Torvik fractional differential equation

• Autorzy: Svatoslav Staněk
• Języki publikacji: EN

Abstrakty

EN

We investigate the fractional differential equation u″ + A c D α u = f(t, u, c D μ u, u′) subject to the boundary conditions u′(0) = 0, u(T)+au′(T) = 0. Here α ∈ (1, 2), µ ∈ (0, 1), f is a Carathéodory function and c D is the Caputo fractional derivative. Existence and uniqueness results for the problem are given. The existence results are proved by the nonlinear Leray-Schauder alternative. We discuss the existence of positive and negative solutions to the problem and properties of their derivatives.

Słowa kluczowe

EN

Fractional differential equation; Bagley-Torvik fractional equation; Caputo derivative; Boundary value problem; Existence; Uniqueness; Positive solution; Negative solution; Nonlinear Leray-Schauder alternative

Kategorie tematyczne

• 34B15: Nonlinear boundary value problems
• 34A08: Fractional differential equations

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 3
• Strony: 574-593

Daty

wydano

2013-03-01

online

2012-12-22

Twórcy

autor

Svatoslav Staněk

• Department of Mathematical Analysis, Faculty of Science, Palacký University, 17. listopadu 12, 771 46, Olomouc, Czech Republic

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-012-0141-4