| Summary: | Abstract This paper investigates the existence of denumerably many positive solutions and two infinite families of positive solutions for the n-dimensional higher-order fractional differential system D0+αx(t)+λg(t)f(t,x(t))=0 $\mathbf{D}_{0^{+}}^{\alpha}\mathbf{x}(t)+\lambda \mathbf{g}(t)\mathbf{f}(t,\mathbf{x}(t))=0$, 0<t<1 $0< t<1$. The vector-valued function x is defined by x=[x1,x2,…,xn]⊤ $\mathbf {x}=[x_{1},x_{2},\dots,x_{n}]^{\top}$, g(t)=diag[g1(t),g2(t),…,gn(t)] $\mathbf{g}(t)=\operatorname{diag}[g_{1}(t), g_{2}(t), \ldots, g_{n}(t)]$, where gi∈Lp[0,1] $g_{i}\in L^{p}[0,1]$ for some p≥1 $p\geq 1$, i=1,2,…,n $i=1,2,\ldots, n$, and has infinitely many singularities in [0,12) $[0,\frac{1}{2})$. Our methods employ the fixed point theorems combined with the partially ordered structure of a Banach space.
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