Abstract. In this paper, we investigate the existence of solutions in Gauge spaces for the nonlinear fractional differential equation boundary value problem With different boundary value and and different order 1 < a  2 and 0 < a < 1. where 0 < /31 < /32 < T and µ  [O, T]and + is the standard Riemann-Lowville differentiation with f(t, u(t))  C([O, T] x [O,  ), R). By using some fixed-point results on gauge spaces, some existence results of positive solutions are obtained.