TY - JOUR
T1 - Existence of Solutions for Nonlocal Boundary Value Problem of Fractional Differential Equations on the Infinite Interval
AU - Aoun , Abdellatif Ghendir
JO - Annals of Applied Mathematics
VL - 4
SP - 340
EP - 352
PY - 2022
DA - 2022/06
SN - 33
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/aam/20615.html
KW - boundary value problem, fractional differential equation, infinite interval, nonlocal condition, fixed point theorem.
AB - <p style="text-align: justify;">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 $1&lt;α\leq 2,$ $^cD^α_{0+}$ 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.</p>