Editing Fractional-order integrator (section)

{{further|Fractional calculus}}{{More citations needed|date=March 2025}}{{calculus|expanded=Specialized calculi}}
A '''fractional-order integrator''' or just simply '''fractional integrator''' is an [[integrator]] device that calculates the fractional-order integral or derivative (usually called a [[differintegral]]) of an input. Differentiation or integration is a real or complex parameter. The fractional integrator is useful in [[fractional-order control]] where the history of the system under control is important to the control system output.{{Citation needed|date=March 2025}}

Some industrial controllers use fractional-order [[PID controller|PID controllers]] (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.<ref>{{Cite journal |last=Tolba |first=Mohammed F. |last2=AboAlNaga |first2=BahaaAlDeen M. |last3=Said |first3=Lobna A. |last4=Madian |first4=Ahmed H. |last5=Radwan |first5=Ahmed G. |date=2019-01-01 |title=Fractional order integrator/differentiator: FPGA implementation and FOPID controller application |url=https://www.sciencedirect.com/science/article/abs/pii/S1434841118308185 |journal=AEU - International Journal of Electronics and Communications |volume=98 |pages=220–229 |doi=10.1016/j.aeue.2018.10.007 |issn=1434-8411|url-access=subscription }}</ref>