  In the present paper, we determine the estimations on Atangana-Baleanu-Caputo
fractional derivative at extreme points. With the assistance of the estimations
obtained, we derive the comparison results. Peano's type existence results
established for nonlinear fractional differential equations involving
Atangana-Baleanu-Caputo fractional derivative. The acquired comparison results
are then utilized to deal with the existence of local, extremal and global
solution.
