Spline left fractional monotone approximation involving left fractional differential operators
Author
Anastassiou, George A.
Full text
https://revistas.ufro.cl/ojs/index.php/cubo/article/view/115110.4067/S0719-06462015000100005
Abstract
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).