Multiplicity of positive solutions of a class of nonlinear fractional differential equations

where L(D) = Dsn − an−1Dsn−1 − … − a1Ds11 < s2 < … < sn < 1, and aj > 0, j = 1,2,…, n − 1. Some results are obtained for the existence, nonexistence, and multiplicity of positive solutions of the above equation by using Krasnoselskii's fixed-point theorem in a cone. In particular, it is proved that the above equation has N positive solutions under suitable conditions, where N is an arbitrary positive integer.