Spline left fractional monotone approximation involving left fractional differential operators
Let f ? Cs ([-1, 1]), s? N and L* be a linear left fractional differential operator such that L* (f) = 0 on [0, 1]. Then there exists a sequence Qn, n ?<img border=0 width=19 height=19 src="http:/fbpe/img/cubo/v17n1/art05-1.jpg"> of polynomial spli...
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Universidad de La Frontera. Departamento de Matemática y Estadística.
2015
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oai:scielo:S0719-064620150001000052018-10-08Spline left fractional monotone approximation involving left fractional differential operatorsAnastassiou,George A Monotone Approximation Caputo fractional derivative fractional linear differential operator modulus of smoothness splines Let f ? Cs ([-1, 1]), s? N and L* be a linear left fractional differential operator such that L* (f) = 0 on [0, 1]. Then there exists a sequence Qn, n ?<img border=0 width=19 height=19 src="http:/fbpe/img/cubo/v17n1/art05-1.jpg"> 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).info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.17 n.1 20152015-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462015000100005en10.4067/S0719-06462015000100005 |
| institution |
Scielo Chile |
| collection |
Scielo Chile |
| language |
English |
| topic |
Monotone Approximation Caputo fractional derivative fractional linear differential operator modulus of smoothness splines |
| spellingShingle |
Monotone Approximation Caputo fractional derivative fractional linear differential operator modulus of smoothness splines Anastassiou,George A Spline left fractional monotone approximation involving left fractional differential operators |
| description |
Let f ? Cs ([-1, 1]), s? N and L* be a linear left fractional differential operator such that L* (f) = 0 on [0, 1]. Then there exists a sequence Qn, n ?<img border=0 width=19 height=19 src="http:/fbpe/img/cubo/v17n1/art05-1.jpg"> 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). |
| author |
Anastassiou,George A |
| author_facet |
Anastassiou,George A |
| author_sort |
Anastassiou,George A |
| title |
Spline left fractional monotone approximation involving left fractional differential operators |
| title_short |
Spline left fractional monotone approximation involving left fractional differential operators |
| title_full |
Spline left fractional monotone approximation involving left fractional differential operators |
| title_fullStr |
Spline left fractional monotone approximation involving left fractional differential operators |
| title_full_unstemmed |
Spline left fractional monotone approximation involving left fractional differential operators |
| title_sort |
spline left fractional monotone approximation involving left fractional differential operators |
| publisher |
Universidad de La Frontera. Departamento de Matemática y Estadística. |
| publishDate |
2015 |
| url |
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462015000100005 |
| work_keys_str_mv |
AT anastassiougeorgea splineleftfractionalmonotoneapproximationinvolvingleftfractionaldifferentialoperators |
| _version_ |
1714206791767687168 |