On the solutions to a Riemann-Liouville fractional q-derivative boundary value problem

Abstract Within the framework of q -fractional calculus, we study a nonlinear fractional differential equation conditioned by values that contain a parameter and a q -integral. Using a combination of various techniques, among which some convenient upper and lower solutions stand out, as well as different convexity and contraction methods, several conditions are found to guarantee the existence of one, two or three positive solutions to the problem under consideration.