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In this paper a discrete time approximation of Caputo's fractional order derivatives is used for modeling the dynamic behavior of hypothetical fractional order systems the appropriate responses of which that can directly be manipulated by some physical agents are some fractional order time-derivatives of their state variables. A possible generalization of the concept of ldquoinitial conditionsrdquo...
In this paper we propose a modified version of the classical unforced Van der Pol oscillator that occurs when introducing a fractional-order time derivative in the state space equations that describes its dynamics. The resulting fractional-order Van der Pol oscillator is analyzed in the time and frequency domains, for several values of order's fractional derivative and, consequently, of the total...
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