Let $fin C^{r}left( left[ -1,1ight] ight) $, $rgeq 0$ and let $ L^{st }$ be a linear left fractional differential operator such that $ L^{st }left( fight) geq 0$ throughout $left[ 0,1ight] $. We can find a sequence of polynomials $Q_{n}$ of degree $leq n$ such that $L^{st }left( Q_{n}ight) geq 0$ over $left[ 0,1ight] $, furthermore $f$ is approximated left fractionally and simultaneously by $Q_{n}$ on $left[ -1,1 ight] .$ The degree of these restricted approximations is given via inequalities using a higher order modulus of smoothness for $f^{left( right) }.$
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机译：设$ f in C ^ {r} left（ left [-1,1 right] right）$，$ r geq 0 $并令$ L ^ { ast} $为线性左分数微分使得$ L ^ { ast} left（f right） geq 0 $贯穿$ left [0,1 right] $。我们可以找到度为$ leq n $的多项式$ Q_ {n} $的序列，使得$ L ^ { ast} left（Q_ {n} right） geq 0 $超过$ left [0， 1 right] $，此外，$ f_被$ Q_ {n} $在$ left [-1,1 right]上小数并同时逼近。这些受限制逼近的程度通过不等式使用更高的$ f ^ { left（r right）}。$的平滑阶模量
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