Fermatean　fuzzy　sets　are　an　effective　way　to　handle　uncertainty　and　vagueness　by　expanding　the　spatial　scope　of　membership　and　nonmembership　of　the　intuitionistic　fuzzy　set　and　the　Pythagorean　fuzzy　set.　However,　existing　studies　only　analyzed　the　discrete　information　and　neglected　the　continuous　state　of　Fermatean　fuzzy　sets.　In　this　paper,　we　investigated　the　properties　of　continuous　Fermatean　fuzzy　information　by　firstly　proposing　Fermatean　fuzzy　functions,　then　defining　the　subtraction　and　division　operations　of　Fermatean　fuzzy　functions　and　discussing　their　properties.　Further,　we　examined　the　continuity,　deriva-tives,　and　differentials　of　Fermatean　fuzzy　functions.　Effective　approximate　calculations　regarding　nonlinear　problems　in　the　Fermatean　fuzzy　environment　were　provided,　and　some　examples　were　presented　to　verify　the　feasibility　and　effectiveness　of　approximate　calculations　using　the　Fermatean　fuzzy　functions.　©　2021　The　Authors.　Published　by　Atlantis　Press　B.V.