In this paper, by using a fixed point theorem, we investigate the existence of a positive solution to the singular fractional boundary value problem D C 0 + α u + f t , u , D C 0 + ν u , D C 0 + μ u + g t , u , D C 0 + ν u , D C 0 + μ u = 0 , u 0 = u ′ 0 = u ′ ′ 0 = u ′ ′ ′ 0 = 0 , where 3 < α < 4 , 0 < ν < 1 , 1 < μ < 2 , D C 0 + α is Caputo fractional derivative, f t , x , y , z is singular at the value 0 of its arguments x , y , z , and g t , x , y , z satisfies the Lipschitz condition.