In　this　paper,　a　type　of　fractional-order　quaternion-valued　neural　networks　(FOQVNNs)　with　leakage　and　time-varying　delays　is　established　to　simulate　real-world　situations,　and　the　global　Mittag-Leffler　stability　of　the　system　is　investigated　by　using　the　non-decomposition　method.　First,　to　avoid　decomposing　the　system　into　two　complex-valued　systems　or　four　real-valued　systems,　a　new　sign　function　for　quaternion　numbers　is　introduced　based　on　the　ones　for　real　and　complex　numbers.　And　two　novel　lemmas　for　quaternion-valued　sign　function　and　Caputo　fractional　derivative　are　established　in　quaternion　domain,　which　are　used　to　investigate　the　stability　of　FOQVNNs.　Second,　a　concise　and　flexible　quaternion-valued　state　feedback　controller　is　directly　designed　and　a　novel　1-norm　Lyapunov　function　composed　of　the　absolute　values　of　real　and　imaginary　parts　is　established.　Then,　based　on　the　designed　quaternion-valued　state　feedback　controller　and　the　proposed　lemmas,　some　sufficient　conditions　are　given　to　ensure　the　global　Mittag-Leffler　stability　of　the　system.　Finally,　a　numerical　simulation　is　given　to　verify　the　theoretical　results.　(C)　2021　Elsevier　Ltd.　All　rights　reserved.