Abstract
We deal with the following Riemann-Liouville fractional nonlinear boundary value problem:
integral D(alpha)v(x) + f (x, v(x)) = 0, 2 < alpha <= 3, x is an element of (0, 1),
v(0) = v'(0) = v(1) = 0.
Under mild assumptions, we prove the existence of a unique continuous solution v to this problem satisfying
vertical bar v(x)vertical bar <= cx(alpha-1)(1 - x) for all x is an element of [0, 1] and some c > 0.
Our results improve those obtained by Zou and He (Appl. Math. Lett. 74:68-73, 2017).