Abstract
This paper examines three new definitions of the fractional derivative with singular and non-singular kernels in an eco-epidemics model of predator-prey type. The model describes the situation in which an infectious disease has been spread in the predator category that affects all other interactions in the system. Moreover, equilibrium points related to the model are identified and conditions related to the stability of each are stated. Further, several simulated scenarios have been provided to support the analytical discussions. The sensitivity of the models to changes in some parameters in them has been investigated and it was seen that these changes sometimes cause chaos in the studied dynamic systems. The utilized techniques in this contribution will enable us to handle other related eco-epidemics models including fractional-derivative operators in an accurate and efficient manner.