Summary: We study the following boundary value problem of the fractional order differential equation
where , and may be singular at or/and at , is the standard Riemann-Liouville differentiation, is nonnegative, and .
The expression and properties of Green’s function are studied and employed to obtain some results on the existence of positive solutions by using a fixed point theorem in cones. The proofs are based on the reduction of the problem considered to the equivalent Fredholm integral equation of the second kind. The results significantly extend and improve many known results even for integer-order cases.