Rotating and non-linear magnetic-charged black hole surrounded by quintessence

In this work we derived a rotating and non-linear magnetic-charged black hole surrounded by quintessence using the Newman-Janis algorithm. Considering the state parameter $\omega_q=-3/2$, we studied the event horizons, the ergosphere, and the ZAMO. We found that the existence of the outer horizon is constrained by the values of the charge $Q$. Furthermore, we found that the ergo-region increases when both the charge $Q$ and the spin parameter $a$ are increased. On the other hand, regarding equatorial circular orbits, we studied the limit given by the static radius on the existence of circular geodesics, the photon circular geodesics, and the innermost stable circular orbits (ISCO). We show that photon circular orbits do not depend strongly on $Q$, and $r_{ISCO}$ is constrained by the values of charge.