Positive solutions for nonlinear fractional differential equations with coefficient that changes sign

In this paper, we investigate the existence of positive solutions in case of the nonlinear fractional differential equationDsu=λa(t)f(u),00f(0)>0, a:[0,1]→(-∞,+∞)a:[0,1]→(-∞,+∞) may change sign, and λ>0λ>0 is a parameter. Our analysis relies on a nonlinear alternative of Leray–Schauder type.