Abstract
The victim-predator model has been investigated in several papers in the literature since it is considered one of the very important models. The relation between predator and victim is an important aspect of ecology. The principal object of this research is to propose a new Caputo fractional one victim-two predators model with variable parameters. In addition, we study its stability and prove the existence and uniqueness of its solution. We calculate its approximate solution using Laplace transform coupled with the Adomian Decomposition Method (ADM) in two cases. Also, in order to complete the study of the proposed paradigm, we simulate and show its fractional dynamics plus the effect of changing certain parameters on its fractional dynamics against various fractional orders.
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