This　paper　introduces　fractional　Brownian　motion　into　the　study　of　Maxwell　nanofluids　over　a　stretching　surface.　Nonlinear　coupled　spatial　fractional-order　energy　and　mass　equations　are　established　and　solved　numerically　by　the　finite　difference　method　with　Newton’s　iterative　technique.　The　quantities　of　physical　interest　are　graphically　presented　and　discussed　in　detail.　It　is　found　that　the　modified　model　with　fractional　Brownian　motion　is　more　capable　of　explaining　the　thermal　conductivity　enhancement.　The　results　indicate　that　a　reduction　in　the　fractional　parameter　leads　to　thinner　thermal　and　concentration　boundary　layers,　accompanied　by　higher　local　Nusselt　and　Sherwood　numbers.　Consequently,　the　introduction　of　a　fractional　Brownian　model　not　only　enriches　our　comprehension　of　the　thermal　conductivity　enhancement　phenomenon　but　also　amplifies　the　efficacy　of　heat　and　mass　transfer　within　Maxwell　nanofluids.　This　achievement　demonstrates　practical　application　potential　in　optimizing　the　efficiency　of　fluid　heating　and　cooling　processes,　underscoring　its　importance　in　the　realm　of　thermal　management　and　energy　conservation.　©　2024　by　the　authors.