In this paper we prove existence and approximation of the solutions for initial value problems of nonlinear hybrid fractional differential equations with maxima and with a linear as well as quadratic perturbation of second type. The main results rely on Dhage iteration method embodied in the recent hybrid fixed point theorem of Dhage (2014) in a partially ordered normed linear space. The approximation of the solutions of the considered nonlinear fractional differential equations are obtained under weaker mixed partial continuity and Lipschitz conditions. Our hypotheses and the main results are also illustrated by a numerical example.
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