Nanoparticles　have　gained　recognition　for　significantly　improving　convective　heat　transfer　efficiency　near　boundary　layer　flows.　The　characteristics　of　both　momentum　and　thermal　boundary　layers　are　significantly　influenced　by　the　Prandtl　number,　which　holds　a　crucial　role.　In　this　vein,　the　current　study　conducted　a　detailed　computational　analysis　of　the　mixed　convection　flow　of　gamma-Al2O3　and　gamma-Al2O3-C2H6O2　nanofluids　over　a　stretching　surface.　This　research　integrates　an　effective　Prandtl　number,　utilizing　viscosity　and　thermal　conductivity　models　based　on　empirical　findings.　Additionally,　a　unique　double-fractional　constitutive　model　is　debuted　to　accurately　evaluate　the　effective　Prandtl　number＇s　function　in　the　boundary　layer.　The　equations　were　solved　using　a　numerical　technique　that　combined　the　finite-difference　method　with　the　L-1　algorithm.　This　investigation　presents　numerical　findings　related　to　the　velocity,　temperature　distributions,　wall　shear　stress　coefficient,　and　heat　transfer　coefficient,　contrasting　scenarios　with　and　without　the　effective　Prandtl　number.　The　research　shows　that　integrating　nanoparticles　into　the　base　fluids　reduces　the　temperature　of　the　nanofluid　with　an　effective　Prandtl　number　while　enhancing　the　heat　transfer　rate　irrespective　of　its　presence.　Nonetheless,　the　introduction　of　a　fractional　parameter　reduced　the　heat　transfer　efficiency　within　the　system.　Notably,　the　gamma-Al2O3-C2H6O2　nanofluid　demonstrates　superior　heat　transfer　enhancement　capabilities　compared　to　its　gamma-Al2O3　counterpart　but　also　exacerbates　the　drag　coefficient　more　significantly.　Many　practical　applications　of　this　study　include　electronics　cooling,　industrial　process　heat　exchangers,　and　rotating　and　stationary　gas　turbines　in　power　plants,　and　efficient　heat　exchangers　in　aircraft.