Many　studies　have　proved　that　the　fractional-order　system　is　more　accurate　than　the　integer-order　system.　The　theory　of　fractional　calculus　has　received　extensive　attention　in　many　fields.　The　research　on　flux-controlled　memristor　has　been　carried　out　for　several　years;　however,　fractional-order　flux-controlled　memristor　has　not　received　widespread　attention.　In　light　of　the　theory　of　fractional　calculus,　a　generalized　fractional-order　dynamic　model　of　flux-controlled　memristor　is　proposed　for　the　first　time　in　this　paper.　The　mathematical　model　is　established　and　its　characteristics　of　the　pinched　hysteresis　loops　are　analyzed　by　changing　the　order　and　the　frequency.　The　specific　computational　formulas　of　areas　of　pinched　hysteresis　loops　are　given.　The　equivalent　circuit　of　the　fractional-order　flux-controlled　memristor　is　constructed,　and　circuit　simulations　are　given　to　illustrate　the　effectiveness　of　theoretical　analysis　and　numerical　calculation.　In　this　study,　the　flux-controlled　memristor　model　is　extended　to　the　fractional-order　model　that　is　closer　to　the　real　device,　and　the　analysis　method　of　areas　of　pinched　hysteresis　loops　is　further　expanded.