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.
@article{bwmeta1.element.doi-10_2478_s11533-012-0141-4,
author = {Svatoslav Stan\v ek},
title = {Two-point boundary value problems for the generalized Bagley-Torvik fractional differential equation},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {574-593},
zbl = {1262.34008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0141-4}
}
Svatoslav Staněk. Two-point boundary value problems for the generalized Bagley-Torvik fractional differential equation. Open Mathematics, Tome 11 (2013) pp. 574-593. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0141-4/
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