Lower and Upper Solutions for General Two-Point Fractional Order Boundary Value Problems

Abstract

This paper establishes the existence of a positive solution of fractional order two-point boundary value problem, D q1 a+ y t + f t, y t = 0, t ∈ [a, b], y a = 0, y ′ a = 0, αDq2 a+ y b − βDq3 a+ y a = 0, where D qi a+ , i = 1, 2, 3 are the standard Riemann-Liouville fractional order derivatives, 2 a ≥ 0, by an application of lower and upper solution method and fixed-point theorems