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The anomalous $ZZ\gamma$ and $Z\gamma\gamma$ neutral triple gauge couplingsoccurred by dimension-eight operators are investigated through the process$\mu^+\mu^-\,\rightarrow\,\mu^+\gamma^*\mu^-\,\rightarrow\,\mu^+Z(\nu\bar{\nu})\mu^-$ at the muon collider with $\sqrt{s}=3$, $6$, $10$ and$14$ TeV. The charged lepton pseudo-rapidity, the charged lepton transversemomentum and the transverse missing energy distributions are taken inconsideration for the final state of the process in the analysis. Thesensitivities of the anomalous couplings are obtained at $95\%$ ConfidenceLevel with integrated luminosity of ${\cal L}_{\text{int}}=1$, $4$, $10$ and$20$ ab$^{-1}$, respectively, according to center-of-mass energies of muoncollider taking into account the effects of systematic uncertainties $0\%$,$3\%$ and $5\%$. The best limits of anomalous $C_{BB}/{\Lambda^4}$,$C_{BW}/{\Lambda^4}$, $C_{\widetilde{B}W}/{\Lambda^4}$ and $C_{WW}/{\Lambda^4}$couplings without systematic uncertainty at center-of-mass energy of 14 TeV andintegrated luminosity of 20 ab$^{-1}$ are found to be [-0.01026; 0.00636]TeV$^{-4}$, [-0.02482; 0.03053] TeV$^{-4}$, [-0.01830; 0.02510] TeV$^{-4}$,[-0.06981; 0.07387] TeV$^{-4}$, respectively.

Probe of the anomalous neutral triple gauge couplings in photon-induced collision at future muon colliders