In the current study according to the proper understanding o f the Atangana-Baleanu fractional derivative in the Caputo sense, a novel and fundamental approach is presented as an extensio ns of existence and uniqueness theorems of ordinary fractio nal difference (FDE) which was applied to the reducing Cauchy type problems (CTP). Results give a new interpretation in order for analyz ing the fractional calculus which implies an elegant superiority o f the suggested derivative.
