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We analyze the quasi-periodic oscillation (QPO) of the historical light curveof FSRQs PKS 0405-385 detected by the Fermi LAT from August 2008 to November2021. To identify and determine the QPO signal of PKS 0405-385 in the$\gamma$-ray light curve, we use four time series analysis techniques based onfrequency and time domains, i.e., the Lomb-Scargle periodogram (LSP), theweighted wavelet z-transform (WWZ), the REDFIT and the epoch folding. Theresults show that PKS 0405-385 has a quasi-periodic behavior of $\sim$2.8 yrwith the significance of $\sim$4.3$\sigma$ in Fermi long-term monitoring.Remarkably, we also performed QPO analysis in the G-band light curve observedfrom October 2014 to October 2021 using LSP and WWZ technology, and the results($\sim$4$\sigma$ of significance) are consistent with the periodic detection in$\gamma$-ray. This may imply that the optical emission is radiated by anelectron population same as the \gr\ emission. In discussing the possiblemechanism of quasi-periodic behavior, either the helical motion within a jet orthe supermassive black hole binary system provides a viable explanation for theQPO of 2.8 yr, and the relevant parameters have been estimated.

Quasi-periodic behaviour in the $\gamma$-ray light curve of the blazar PKS 0405-385