Abstract            

A fractional-order predator–prey biological
economic system with Holling type II functional
response is proposed. Local stability and Hopf bifurcation
of predator–prey systems have been investigated
in both commensurate and incommensurate fractionalorder
systems.We explore howthe economic profit and
fractional orders influence the local stability and Hopf
.bifurcation for the fractional-order predator–prey system
For an incommensurate system, we propose a new
theory for the existence of Hopf bifurcation when the
.fractional orders are considered as bifurcation parameters
Several numerical examples are demonstrated to
.validate the theoretical results