Inthisarticle,theexistenceanduniquenessofpositivesolutionforaclassofnonlinearfractionaldifferentialequationsisprovedbyconstructingtheupperandlowercontrolfunctionsofthenonlineartermwithoutanymonotonerequirement.OurmainmethodtotheproblemisthemethodofupperandlowersolutionsandSchauderfixedpointtheorem.Finally,wegiveanexampletoilluminateourresults.