Proposal for Use the Fractional Derivative of Radial Functions in Interpolation Problems

A. Torres-Hernandez, F. Brambila-Paz, C. Torres-Martínez

In this document we present the construction of a radial functions that have the objective of emulating the behavior of the radial basis function thin plate spline (TPS), which we will name as function TPS, we propose a way to partially and totally apply the fractional derivative to these functions to be used in interpolation problems, a proposal is presented to precondition the matrices generated in the interpolation problem using the $QR$ decomposition and finally is proposed the form of a radial interpolant to be used when solving differential equations using the asymmetric collocation method.

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