The generalized Grünwald–Letnikov fractional derivative is analyzed in this paper. Its Laplace and Fourier transforms are computed, and some current results are criticized. It is shown that only the forward derivative of a sinusoid exists. This result is used to define the frequency response of a fractional linear system.

Issue Section:
Technical Briefs
Keywords:
fractional difference, fractional derivative, fractional linear system, differintegrator, Fourier transforms, Laplace transforms
Topics:
Fourier transforms, Linear systems
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