JOURNAL BROWSE
Search
Advanced SearchSearch Tips
UNIVARIATE LEFT FRACTIONAL POLYNOMIAL HIGH ORDER MONOTONE APPROXIMATION
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
UNIVARIATE LEFT FRACTIONAL POLYNOMIAL HIGH ORDER MONOTONE APPROXIMATION
Anastassiou, George A.;
  PDF(new window)
 Abstract
Let ([-1,1]), and let be a linear left fractional differential operator such that throughout [0, 1]. We can find a sequence of polynomials of degree such that over [0, 1], furthermore f is approximated left fractionally and simulta-neously by on [-1, 1]. The degree of these restricted approximations is given via inequalities using a higher order modulus of smoothness for .
 Keywords
monotone approximation;Caputo fractional derivative;fractional linear differential operator;higher order modulus of smoothness;
 Language
English
 Cited by
 References
1.
G. A. Anastassiou, Bivariate Monotone Approximation, Proc. Amer. Math. 112 (1991), no. 4, 959-964. crossref(new window)

2.
G. A. Anastassiou, Higher order monotone approximation with linear differential operators, Indian J. Pure Appl. Math. 24 (1993), no. 4, 263-266.

3.
G. A. Anastassiou and O. Shisha, Monotone approximation with linear differential operators, J. Approx. Theory 44 (1985), no. 4, 391-393. crossref(new window)

4.
K. Diethelm, The Analysis of Fractional Differential Equations, Lecture Notes in Mathematics, Vol. 2004, 1st edition, Springer, New York, Heidelberg, 2010.

5.
H. H. Gonska and E. Hinnemann, Pointwise estimates for approximation by algebraic polynomials, Acta Math. Hungar. 46 (1985), no. 3-4, 243-254. crossref(new window)

6.
O. Shisha, Monotone approximation, Pacific J. Math. 15 (1965), 667-671. crossref(new window)