Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
837793 | Nonlinear Analysis: Real World Applications | 2012 | 9 Pages |
Abstract
Using the Mellin transform approach, it is shown that, in contrast with integer-order derivatives, the fractional-order derivative of a periodic function cannot be a function with the same period. The three most widely used definitions of fractional-order derivatives are taken into account, namely, the Caputo, Riemann–Liouville and Grunwald–Letnikov definitions. As a consequence, the non-existence of exact periodic solutions in a wide class of fractional-order dynamical systems is obtained. As an application, it is emphasized that the limit cycle observed in numerical simulations of a simple fractional-order neural network cannot be an exact periodic solution of the system.
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Authors
Eva Kaslik, Seenith Sivasundaram,