Positive solutions for a class of nonlinear fractional differential equations with derivative terms

Abstract

We deal with the existence of positive solutions for nonlinear fractional differential equations whose nonlinearity contains the first-order derivative in a Banach space $E$. Under the superlinear and sublinear growth of nonlinear $f$, which contains the first-order derivative, we obtain the existence of positive solutions. Our discussion is based on the fixed point index theory of condensing mapping in cones.