Positive solution for fractional q-difference boundary value problems with ∅-laplacian operator

In this paper, we investigate the existence of at least one positive solution for a class of fractional q-difference boundary value problems with ?-Laplacian operator. The arguments mainly rely on the upper and lower solutions method as well as the Schauder’s fixed point theorem. Nonlinear term may be singular at t = 0,1 or u = 0. Furthermore, two examples are presented to illustrate the main results.