Abstract: The author considered  a class of singular nonlinear Riemann-Liouville boundary value problems of fractional differential equations, by using the Leggett-Williams fixed point theorem and constructing the  corresponding auxiliary problems with the help of regularization method, it is obtained that there are at least three positive solutions to the boundary value problem, and these positive solutions are also positive solutions to the auxiliary problem.

Key words: singular fractional differential equation, boundary value problem, fixed point theorem, positive solution, existence