Three Positive Solutions of Sturm–liouville Boundary Value Problems for Fractional Differential Equations

We establish the results on the existence of three positive solutions to Sturm-Liouville boundary value problems of the singular fractional differential equation with the nonlinearity depending on D 0+u ⎪⎨ ⎪⎩ D0+u(t)+ f (t,u(t),D μ 0+ u(t)) = 0, t ∈ (0,1),1 < α < 2, a limt→0 I2−α 0+ u(t)−b limt→0 [ I2−α 0+ u(t) ]′ = ∫ 1 0 g(s,u(s),D μ 0+u(s))ds, c D 0+u(1)+du(1) = ∫ 1 0 h(s,u(s),D μ 0+u(s))ds. Our analysis relies on the well known five functional fixed point theorems. An example is given to illustrate the efficiency of the main theorems. Mathematics subject classification (2010): 47J05, 92D25, 34A08, 34A37, 34K15.