An Interpolation Method That Minimizes an Energy Integral of Fractional Order

  • H. Gunawan
  • F. Pranolo
  • E. Rusyaman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5081)


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 \(E_\alpha(u) := \int_0^1 |u^{(\alpha)}(x)|^2 dx\), 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.


Fractional Derivative Interpolation Method Piecewise Linear Function Minimum Solution Energy Integral 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • H. Gunawan
    • 1
  • F. Pranolo
    • 1
  • E. Rusyaman
    • 2
  1. 1.Analysis and Geometry Group, Faculty of Mathematics and Natural SciencesBandung Institute of TechnologyBandungIndonesia
  2. 2.Department of Mathematics, Faculty of Mathematics and Natural SciencesPadjadjaran UniversityBandungIndonesia

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