Recently, a general framework of fractional operators, that includes the Caputo model as a particular case, has been introduced and some applications in the area of fractional calculus have been presented. In this paper, novel fractional epidemic models with generalized Caputo-type derivatives were proposed. The universal predictor-corrector method was modified here to deal with the considered epidemic models for the purposes of simulation. The behavior and complex dynamic of these hybrid fractional epidemic models were studied using the modified method. The dynamics of the generalized Caputo-type fractional SIR, HIV and SEIR models were investigated by numerical simulation. Basically, the effect of generalized Caputo-type fractional derivative operator parameters on the dynamic behavior of the proposed epidemic models was discussed.