Existence of positive solutions to boundary value problem for a nonlinearfractional differential equations

The existence of positive solutions to a boundary value problem for a nonlinear fractional differential equation is investigated. The main method is a local application of Krasnosel'skii fixed-point theorem of cone expansion-compression type. The main results show that the boundary value problem has at least $n$ positive solutions provided that the "height" is appropriate on some bounded sets ($n$ is a positive integer number arbitrarily given )