We deal with the existence of positive solutions for nonlinear fractional differential equations whose nonlinearity contains the first-order derivative in a Banach space . Under the superlinear and sublinear growth of nonlinear , 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.
Haide Gou. "Positive solutions for a class of nonlinear fractional differential equations with derivative terms." Rocky Mountain J. Math. 52 (5) 1619 - 1641, October 2022. https://doi.org/10.1216/rmj.2022.52.1619