Positive solutions for integral nonlinear boundary value problem in fractional Sobolev spaces

In the present paper, we consider an important problem from the point of view of application in sciences and engineering, namely, Riemann–Liouville nonlinear fractional boundary value problem. Under new minimal conditions on the parameters 0 ≤ s, τ ≤ 1, it is shown that, based on the upper and lower solutions method using Schauder fixed point theorem, the positive solutions in a Sobolev spaces exist. Moreover, our results are illustrated by a numerical example.