Existence of Solutions for Nonlocal Boundary Value Problem of Fractional Differential Equations on the Infinite Interval
Year: 2017
Author: Abdellatif Ghendir Aoun
Annals of Applied Mathematics, Vol. 33 (2017), Iss. 4 : pp. 340–352
Abstract
In this paper, we study a fractional differential equation $$^cD^α _{0+} u(t) + f(t, u(t)) = 0, \ t ∈ (0, +∞)$$ satisfying the boundary conditions: $$u′(0)=0,\ \lim\limits_{t→+∞} \ ^cD^{α−1}_{0+} u(t) = g(u),$$ where $1<α\leq 2,$ $^cD^α_{0+}$ is the standard Caputo fractional derivative of order $α.$ The main tools used in the paper is a contraction principle in the Banach space and the fixed point theorem due to D. O’Regan. Under a compactness criterion, the existence of solutions is established.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2017-AAM-20615
Annals of Applied Mathematics, Vol. 33 (2017), Iss. 4 : pp. 340–352
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: boundary value problem fractional differential equation infinite interval nonlocal condition fixed point theorem.