Let f ∈ Cs ([−1, 1]), s∈ IN and L∗ be a linear left fractional differential operator such that L∗(f) ≥ 0 on [0,1]. Then there exists a sequence Qn, n ∈ IN of polynomial splines with equally spaced knots of given fixed order such that L∗ (Qn) ≥ 0 on [0, 1]. Furthermore f is approximated with rates fractionally and simultaneously by Qn in the uniform norm. This constrained fractional approximation on [−1, 1] is given via inequalities invoving a higher modulus of smoothness of f(s).
@article{1151,
title = {Spline left fractional monotone approximation involving left fractional differential operators},
journal = {CUBO, A Mathematical Journal},
volume = {17},
year = {2015},
language = {en},
url = {http://dml.mathdoc.fr/item/1151}
}
Anastassiou, George A. Spline left fractional monotone approximation involving left fractional differential operators. CUBO, A Mathematical Journal, Tome 17 (2015) 9 p. http://gdmltest.u-ga.fr/item/1151/