This　paper　mainly　studies　the　state　of　charge　(SOC)　estimation　of　lithium　batteries　based　on　a　fractional-order　adaptive　square-root　cubature　Kalman　filter　(FO-ASRCKF).　Firstly,　a　fractional-order　model　(FOM)　of　lithium　battery　is　established　by　using　fractional-order　derivative　theory.　In　order　to　meet　the　identification　accuracy,　an　improved　adaptive　genetic　algorithm　is　applied　to　the　process　of　multi-parameter　model　identification.　Then,　the　FO-ASRCKF　algorithm　based　on　FOM　and　adaptive　rules　is　proposed,　and　a　comparative　experiment　with　Fractional-order　adaptive　iterative　extended　Kalman　filter　(FO-AIEKF)　and　Integer-order　adaptive　square-root　cubature　Kalman　filter　(IO-ASRCKF)　is　carried　out.　The　experimental　results　show　that　the　proposed　FO-ASRCKF　can　work　normally　under　various　working　conditions,　and　it　has　higher　SOC　estimation　accuracy,　with　the　mean　absolute　error　(MAE)　being　less　than　0.5%.　Moreover,　it　can　also　overcome　the　divergence　caused　by　noise　and　wrong　initial　values,　indicating　a　better　robustness.　©　2023　Elsevier　Ltd