In this work, we introduce ABC-Caputo operator with ML kernel and its main characteristics are discussed. Viral diseases models for AIDS and Zika are considered, and finally, as third model, the macroeconomic model involving ABC fractional derivatives is investigated, respectively. It is presented that the AB Caputo derivatives satisfy the Lipschitz condition along with superposition property. The numerical methods for solving the fractional models are presented by means of ABC fractional derivative in a detailed manner. Finally the simulation results obtained in this paper according to the suitable values of parameters are also manifested.
