UNIVARIATE LEFT FRACTIONAL POLYNOMIAL HIGH ORDER MONOTONE APPROXIMATION

Title & Authors
UNIVARIATE LEFT FRACTIONAL POLYNOMIAL HIGH ORDER MONOTONE APPROXIMATION
Anastassiou, George A.;

Abstract
Let $\small{f{\in}C^r}$ ([-1,1]), $\small{r{\geq}0}$ and let $\small{L^*}$ be a linear left fractional differential operator such that $\small{L^*}$ $\small{(f){\geq}0}$ throughout [0, 1]. We can find a sequence of polynomials $\small{Q_n}$ of degree $\small{{\leq}n}$ such that $\small{L^*}$ $\small{(Q_n){\geq}0}$ over [0, 1], furthermore f is approximated left fractionally and simulta-neously by $\small{Q_n}$ on [-1, 1]. The degree of these restricted approximations is given via inequalities using a higher order modulus of smoothness for $\small{f^{(r)}}$.
Keywords
monotone approximation;Caputo fractional derivative;fractional linear differential operator;higher order modulus of smoothness;
Language
English
Cited by
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