Abstract
In this paper, we are concerned with the following fractional Navier boundary value problem:
D-beta(D(alpha)u)(x) = -g(u), x is an element of(0, 1), lim(x -> 0+) x(1-beta)D(alpha)u(x) - -a, u(1) -b,
where alpha, beta is an element of (0, 1] such that alpha + beta > 1, D-alpha and D-beta stand for the standard Riemann-Liouville fractional derivatives, the function g is continuous and non- increasing on (0, infinity) and the reals a, b is an element of (0, infinity). Using Schauder's fixed point theorem, we prove the existence of positive continuous solutions.