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We investigate the existence and multiplicity of positive solutions for the nonlinear fractional differential equation initial value problem D0+αu(t)+D0+βu(t)=f(t,u(t)), u(0)=0, 0<t<1, where 0<β<α<1, D0+α is the standard Riemann-Liouville differentiation and f:[0,1]×[0,∞)→[0,∞) is continuous. By using some fixed-point results on cones, some existence and multiplicity results of positive solutions are obtained.