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

Svatoslav Staněk

Open Mathematics (2013)

  • Volume: 11, Issue: 3, page 574-593
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Svatoslav Staněk. "Two-point boundary value problems for the generalized Bagley-Torvik fractional differential equation." Open Mathematics 11.3 (2013): 574-593. <http://eudml.org/doc/268947>.

@article{SvatoslavStaněk2013,
abstract = {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.},
author = {Svatoslav Staněk},
journal = {Open Mathematics},
keywords = {Fractional differential equation; Bagley-Torvik fractional equation; Caputo derivative; Boundary value problem; Existence; Uniqueness; Positive solution; Negative solution; Nonlinear Leray-Schauder alternative; fractional differential equation; boundary value problem; existence; uniqueness; positive solution; negative solution; nonlinear Leray-Schauder alternative},
language = {eng},
number = {3},
pages = {574-593},
title = {Two-point boundary value problems for the generalized Bagley-Torvik fractional differential equation},
url = {http://eudml.org/doc/268947},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Svatoslav Staněk
TI - Two-point boundary value problems for the generalized Bagley-Torvik fractional differential equation
JO - Open Mathematics
PY - 2013
VL - 11
IS - 3
SP - 574
EP - 593
AB - 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.
LA - eng
KW - Fractional differential equation; Bagley-Torvik fractional equation; Caputo derivative; Boundary value problem; Existence; Uniqueness; Positive solution; Negative solution; Nonlinear Leray-Schauder alternative; fractional differential equation; boundary value problem; existence; uniqueness; positive solution; negative solution; nonlinear Leray-Schauder alternative
UR - http://eudml.org/doc/268947
ER -

References

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