existence and uniqueness of positive solutions for a class of singular nonlinear fractional differential equations with integral boundary value conditions

^cd^αu(t) + f(t, u(t), u(t), u(t)) = 0, 0 < t < 1,

u(0) = u′′(0) = u′′′(0) = 0, u′(0) + u′(1) = λ∫¹₀u(s)ds,

where 3< α ≤4, 0 < λ < 4, ^cd^α is the caputo fractional derivative and f : (0, 1] × [0,∞) × [0,∞) × [0,∞) _® [0,∞) is continuous, lim_t®0+ f(t, ., ., .) = +∞ (i.e. f is singular at t =0). our analysis is based on a tripled fixed point theorem in partially ordered metric spaces. an example is presented to illustrate the main results.