On the Selection and Meaning of Variable Order Operators for Dynamic Modeling
We review the application of differential operators of noninteger order to the modeling of dynamic systems. We compare all the definitions of Variable Order (VO) operators recently proposed in literature and select the VO operator that has the desirable property of continuous transition between inte...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2010/846107 |
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| Summary: | We review the application of differential operators of noninteger order to
the modeling of dynamic systems. We compare all the definitions of Variable Order
(VO) operators recently proposed in literature and select the VO operator that has
the desirable property of continuous transition between integer and non-integer order
derivatives. We use the selected VO operator to connect the meaning of functional order
to the dynamic properties of a viscoelastic oscillator. We conclude that the order of
differentiation of a single VO operator that represents the dynamics of a viscoelastic
oscillator in stationary motion is a normalized phase shift. The normalization constant
is found by taking the difference between the order of the inertial term (2) and the order
of the spring term (0) and dividing this difference by the angular phase shift between
acceleration and position in radians (𝜋), so that the normalization constant is simply
2/𝜋. |
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| ISSN: | 1687-9643 1687-9651 |