In this paper, we discuss the existence and uniqueness of a positive solution to the following singular fractional differential equation with nonlocal boundary value conditions:

In this paper, we discuss the existence of positive solution to singular fractional differential equations involving Caputo fractional derivative. Necessary and sufficient condition for the existence of C 2 [ 0 , 1 ] positive solution is obtained by means of the fixed point theorems on cones. In addition, the uniqueness results and the iterative sequences of the solution are also given.

In this paper, we consider a Riemann–Liouville type two-term fractional differential equation boundary value problem. Some positive properties of the Green’s function are deduced by using techniques of analysis. As application, we obtain the existence and multiplicity of positive solutions for a fractional boundary value problem under conditions that the nonlinearity $f(t,x)$f(t,x) may change sign and may be singular at $t = 0,1$t=0,1 and $x=0$x=0 , and we also obtain the uniqueness results of positive solution for a singular problem by means of the monotone iterative technique.

In this paper, we consider a class of fractional differential equations with infinite-point boundary value conditions. Under some conditions concerning the spectral radius with respect to the relevant linear operator, both the existence of uniqueness and the nonexistence of positive solution are obtained by means of the iterative technique.