The　vibration　signals　of　faulty　bearings　under　non-stationary　conditions　are　inherently　multi-component　and　time-varying,　which　presents　a　challenge　for　effective　fault　diagnosis.　Considering　the　vibration　characteristics　of　rolling　bearings　under　non-stationary　conditions　and　taking　advantage　of　the　Fractional　Fourier　Transform　(FRFT),　a　novel　diagnosis　method　based　on　the　hypothesis-based　FRFT　has　been　proposed　to　separate　the　fault　components.　First,　the　fault　characteristic　frequencies　(FCFs)　are　extracted　from　the　time-frequency　representation　of　the　vibration　signals,　and　the　Vold-Kalman　filtering　is　employed　to　eliminate　the　influence　of　noises　and　other　interference　components.　Subsequently,　the　fractional　feature　model　is　constructed　to　obtain　speed　information　by　the　hypothesis　approach,　whose　central　idea　is　that　the　rotational　frequency　(RF)-related　frequencies　under　different　fault　types　are　estimated,　based　on　the　extracted　FCFs　and　the　fault　characteristic　orders.　Finally,　fault　diagnosis　is　completed　by　the　RF-related　peaks　in　the　final　spectrum.　The　method　eliminates　the　need　for　rotational　speed　measurement　devices　and　angular　resampling.　Simulation　and　experiment　estimation　results　show　that　the　hypothesis-based　FRFT　method　can　accurately　locate　fault　characteristic　components　of　bearings　under　non-stationary　conditions.　©　2024　IOP　Publishing　Ltd