In this paper, we discuss the existence and uniqueness of solutions for a class of nonlinear fractional quadratic iterative differential equations in Banach space C([0, T], [0, T]),
$$C_{L_T}([0,T],[0,T])$$
, and
$$C_{L_A}([0,T],[0,T])$$
, respectively. Our analysis is based on Schauder’s fixed point theorem, fractional Gronwall inequalities and Picard operator theory. Furthermore, our results can be extend to extra complex nonlinear terms. Finally, some examples are given to illustrate our results.
