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In the fields of dynamical systems and control theory, a fractional-order system is a dynamical system that can be modeled by a fractional differential equation containing derivatives of non-integer order. Fractional-order systems are useful in studying the anomalous behavior of dynamical systems in electrochemistry, biology, viscoelasticity and chaotic systems.〔 == Definition == A general dynamical system of fractional order can be written in the form : where and are functions of the fractional derivative operator of orders and and and are functions of time. A common special case of this is the linear time-invariant (LTI) system in one variable: : The orders and are in general complex quantities, but two interesting cases are when the orders are ''commensurate'' : and when they are also ''rational'': : When , the derivatives are of integer order and the system becomes an ordinary differential equation. Thus by increasing specialization, LTI systems can be of general order, commensurate order, rational order or integer order. 抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Fractional-order system」の詳細全文を読む スポンサード リンク
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