Spline left fractional monotone approximation involving left fractional differential operators

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DOI:

https://doi.org/10.4067/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).

Keywords

Monotone Approximation , Caputo fractional derivative , fractional linear differential operator , modulus of smoothness , splines
  • Pages: 65-73
  • Date Published: 2015-03-01
  • Vol. 17 No. 1 (2015): CUBO, A Mathematical Journal

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Published

2015-03-01

How to Cite

[1]
G. A. Anastassiou, “Spline left fractional monotone approximation involving left fractional differential operators”, CUBO, vol. 17, no. 1, pp. 65–73, Mar. 2015.