Existence of multiple positive solutions of a nonlinear arbitrary order boundary value problem with advanced arguments

In this paper, we investigate nonlinear fractional differential equations of arbitrary order with advanced arguments D 0+u(t) + a(t)f(u(θ(t))) = 0, 0 3 (n ∈ N), D 0+ is the standard Riemann-Liouville fractional derivative of order α, f : [0,∞) → [0,∞), a : [0, 1] → (0,∞) and θ : (0, 1) → (0, 1] are continuous functions. By applying fixed point index theory and Leggett-Williams fixed point theorem, sufficient conditions for the existence of multiple positive solutions to the above boundary value problem are established.