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, Dq1a+ y(t) + f(t, y(t)) = 0, t ∈ [a, b], y(a) = 0, y′(a) = 0, αDq2a+ y(b) − βDq3a+ y(a) = 0, where Dqia+ , i = 1, 2, 3 are the standard Riemann-Liouville fractional order derivatives, 2 < q1 ≤ 3, 0 < q2, q3 < q1, α, β are positive real numbers and b > a ≥ 0, by an application of lower and upper solution method and fixed-point theorems.