In this paper we present a shooting algorithm to solve fractional terminal (or boundary) value problems. The convergence order of the numerical method we describe can be derived based upon properties of the equation being solved and we do not need to impose smoothness conditions on the solution for our analysis. The work is a sequel to our recent investigation where we constructed a nonpolynomial collocation method for the approximation of the solution to fractional initial value problems. Here we show that the method can be adapted for the effective approximation of the solution of terminal value problems. Moreover, we compare the efficiency of this numerical scheme against other existing methods.