Variable-order fractional derivatives and their numerical approximations

Authors:
Duarte Valério;José Sá da Costa
Affiliations:
IDMEC/IST, TULisbon, Portugal;IDMEC/IST, TULisbon, Portugal
Venue:
Signal Processing
Year:
2011

Citing 5
Cited 2

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Abstract

This paper addresses the different possible definitions of variable-order derivatives and their numerical approximations; both approximations based upon the definitions and approximations consisting of non-linear transfer functions (in particular combining existing approximations of constant-order fractional derivatives, such as the Crone approximation, with fuzzy logic) are considered. There are different possible configurations, implementing variable-order fractional derivatives both with and without memory of past values of the time-dependent differentiation order.