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Reference.org
Fractional-order integrator
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<p>A fractional-order integrator or just simply fractional integrator is an <a href="/facts/Integrator/VTqXQuQU">integrator</a> device that calculates the fractional-order integral or derivative (usually called a <a href="/facts/Differintegral/gkWncv4v">differintegral</a>) of an input. Differentiation or integration is a real or complex parameter. The fractional integrator is useful in <a href="/facts/Fractional-order_control/m4GfpGav">fractional-order control</a> where the history of the system under control is important to the control system output. </p><p>Some industrial controllers use fractional-order <a href="/facts/PID_controller/7XcYk0CH">PID controllers</a> (FOPIDs), which have exceeded the performance of standard ones, to the extent that standard ones are sometimes considered as a special case of FOPIDs. Fractional-order integrators and differentiators are the main component of FOPIDs. </p>