Existence of Positive Solutions of Nonlinear Fractional Quadratic Differential Equations

摘要

In this work, we prove the existence as well as approximations of the positive solutions for an initial value problem of nonlinear fractional quadratic differential equations. We use some properties of the Mittag-Leffler functions and its relationship with fractional calculus. Also we obtain some results regarding the existence of positive solutions using the Dhage iterative method embodied in a recent hybrid fixed point theorem of Dhage in partially ordered normed linear spaces.