Vol. 9(2). Jan. 2018, No. 11, pp. 133-140.

ON RIESZ-CAPUTO FRACTIONAL DIFFERENTIATION MATRIX OF RADIAL BASIS FUNCTIONS VIA COMPLEX STEP DIFFERENTIATION METHOD
Vol. 9 (2). July 2018, No. 11, pp. 133-140
SHIKAA SAMUEL, VINOD GILL

Abstract

In literature, evaluation of the fractional differentiation matrix for implementation of radial basis function methods is often achieved via Taylor series expansion. Term by term fractional differentiation of expanded functions usually leads to algebraic complexities and round up errors. This paper focuses on a simplified scheme that evaluates Riesz-Caputo fractional derivative of radial basis functions by applying the complex step differentiation technique. The numerical test example has shown that this approach is more effective and accurate. Furthermore, we solved a two dimensional space fractional system with symmetric Riesz-Caputo fractional derivative using hybrid radial basis function pseudospectral where the fractional differentiation matrices are used for implementation


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