This　paper　is　concerned　with　a　nonlinear　fractional　differential　equation　involving　Caputo　derivative.　By　constructing　the　upper　and　lower　control　functions　of　the　nonlinear　term　without　any　monotone　requirement　and　applying　the　method　of　upper　and　lower　solutions　and　the　Schauder　fixed　point　theorem,　the　existence　and　uniqueness　of　positive　solution　for　the　initial　value　problem　are　investigated.　Moreover,　the　existence　of　maximal　and　minimal　solutions　is　also　obtained.