# Univariate right general high order fractional monotone approximation theory

## Abstract

Here are applied the right general fractional derivatives Caputo type with respect to a base absolutely continuous strictly increasing function g. We mention various examples of such right fractional derivatives for different g. Let f be r-times continuously differentiable function on [a, b], and let L be a linear right general fractional differential operator such that L(f) is non-negative over a critical closed subinterval J of [a, b]. We can find a sequence of polynomials Qn of degree less-equal n such that L(Qn) is non-negative over J, furthermore f is right fractionally and simultaneously approximated uniformly by Qn over [a, b]. The degree of this constrained approximation is given by inequalities employing the high order modulus of smoothness of f(r). We end article with applications of the main right fractional monotone approximation theorem for different g.

## Publication Title

Panamerican Mathematical Journal

## Recommended Citation

Anastassiou, G.
(2015). Univariate right general high order fractional monotone approximation theory.* Panamerican Mathematical Journal**, 25* (4), 1-15.
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