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

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Staněk S.

Open Mathematics

2013

tom 11

nr 3

574-593

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.

Ograniczanie wyników

1 Open Mathematics

1 Staněk S.

1 2013

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