Left general fractional monotone approximation theory

George A. Anastassiou. "Left general fractional monotone approximation theory." Applicationes Mathematicae 43.1 (2016): 117-131. <http://eudml.org/doc/286419>.

@article{GeorgeA2016,
abstract = {We introduce left general fractional Caputo style derivatives with respect to an absolutely continuous strictly increasing function g. We give various examples of such fractional derivatives for different g. Let f be a p-times continuously differentiable function on [a,b], and let L be a linear left general fractional differential operator such that L(f) is non-negative over a closed subinterval I of [a,b]. We find a sequence of polynomials Qₙ of degree ≤n such that L(Qₙ) is non-negative over I, and furthermore f is approximated uniformly by Qₙ over [a,b]. The degree of this constrained approximation is given by an inequality using the first modulus of continuity of $f^\{(p)\}$. We finish with applications of the main fractional monotone approximation theorem for different g. On the way to proving the main theorem we establish useful related general results.},
author = {George A. Anastassiou},
journal = {Applicationes Mathematicae},
keywords = {fractional monotone approximation; general fractional derivative; linear general fractional differential operator; modulus of continuity},
language = {eng},
number = {1},
pages = {117-131},
title = {Left general fractional monotone approximation theory},
url = {http://eudml.org/doc/286419},
volume = {43},
year = {2016},
}

TY - JOUR
AU - George A. Anastassiou
TI - Left general fractional monotone approximation theory
JO - Applicationes Mathematicae
PY - 2016
VL - 43
IS - 1
SP - 117
EP - 131
AB - We introduce left general fractional Caputo style derivatives with respect to an absolutely continuous strictly increasing function g. We give various examples of such fractional derivatives for different g. Let f be a p-times continuously differentiable function on [a,b], and let L be a linear left general fractional differential operator such that L(f) is non-negative over a closed subinterval I of [a,b]. We find a sequence of polynomials Qₙ of degree ≤n such that L(Qₙ) is non-negative over I, and furthermore f is approximated uniformly by Qₙ over [a,b]. The degree of this constrained approximation is given by an inequality using the first modulus of continuity of $f^{(p)}$. We finish with applications of the main fractional monotone approximation theorem for different g. On the way to proving the main theorem we establish useful related general results.
LA - eng
KW - fractional monotone approximation; general fractional derivative; linear general fractional differential operator; modulus of continuity
UR - http://eudml.org/doc/286419
ER -