Abstract
We study the existence, uniqueness, and asymptotic behavior of positive continuous solutions to the fractional Navier boundary-value problem
D-beta(D(alpha)u)(x) = -p(x)u(sigma), is an element of(0,1),
lim(x -> 0) x(1-beta) D(alpha)u(x) = 0, u(1) = 0,
where alpha, beta is an element of (0; 1] such that alpha + beta > 1, D-beta and D-alpha stand for the standard Riemann-Liouville fractional derivatives, sigma is an element of (-1, 1) and p being a nonnegative continuous function in (0, 1) that may be singular at x = 0 and satis fi es some conditions related to the Karamata regular variation theory. Our approach is based on the Schauder fi xed point theorem.