We consider the existence of multiple positive solutions for the following nonlinear fractional differential equations of nonlocal boundary value problems:{D0+αu(t)+f(t,u(t))=0,0t1,u(0)=0,D0+βu(0)=0,D0+βu(1)=∑i=1∞ξiD0+βu(ηi),$$ left { extstyleegin{array}{l} D_{0{+}}^{lpha}u(t)+f(t,u(t))=0, quad 0 t 1, u(0)=0,qquad D_{0{+}}^{eta}u(0)=0,qquad D_{0{+}}^{eta}u(1)=sum_{i=1}^{infty} xi_{i} D_{0{+}}^{eta}u(eta_{i}), end{array}displaystyle ight . $$where2α≤3$2lphaleq3$,1≤β≤2$1leqetaleq2$,α−β≥1$lpha-etageq1$,0ξi,ηi1$0xi_{i}, eta_{i}1$with∑i=1∞ξiηiα−β−11$sum_{i=1}^{infty} xi_{i}eta_{i}^{lpha -eta-1}1$. Existence result of at least two positive solutions is given via fixed point theorem on cones. The nonlinearity f may be singular both on the time and the space variables.
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