An interpolation method that minimizes an energy integral of fractional order
Gunawan H.a, Pranolo F.a, Rusyaman E.b
a Analysis and Geometry Group, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Indonesia
b Department of Mathematics, Faculty of Mathematics and Natural Sciences, Padjadjaran University, Indonesia
Abstract
An interpolation method that minimizes an energy integral will be discussed. To be precise, given N+1 points (x 0,c 0), (x 1,c 1),…, (x N ,c N ) with 0=x 0<x 1<⋯<x N =1 and c 0=c N =0, we shall be interested in finding a sufficiently smooth function u on [0,1] that passes through these N+1 points and minimizes the energy integral , where u (α) denotes the fractional derivative of u of order α. As suggested in [1], a Fourier series approach as well as functional analysis arguments can be used to show that such a function exists and is unique. An iterative procedure to obtain the function will be presented and some examples will be given here. © 2008 Springer-Verlag Berlin Heidelberg.
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Fractional derivatives,Fractional orders,Interpolation methods,Iterative procedures,Smooth functions