In analog circuits we have capacitors, inductors etc..
What is the digital circuit equivalent of these elements which operate in digital values??
For my opinion, the question - in this general form -makes no sense.
Why do you expect that a "circuit equivalent of these elements" does exist in the digital domain?
I think the only possible question in this respect could be:
Which electrical property of a capacitor/inductor could possibly have something like an analogon in the digital domain? Possibly - as some answers imply - the charging process of a capacitor?
But I think there will be no equivalent as far as the voltage-current relationship in the time domain or the impedance characteristic in the frequency domain is concerned.
---------- Post added at 13:18 ---------- Previous post was at 11:42 ----------
Some additional considerations:
A capacitor is a mechanical part with specific electrical properties; "analog" and "digital" are two special methods to process signals. A capacitor can be used in analog working circuits as well as in digital operating circuits, because it can act as a storage element for voltages. Thus, it really makes no sense to ask for a capacitor equivalent for digital applications.
By the way: For my opinion, there are no "digital parts" at all. These parts or circuits, which are believed to be "digital", are operated beween to distinct values only. Between these treshold values there is a (perhaps small) region which behaves "analog". On the other hand, an opamp can be used as a "digital" circuit if operated like a comparator between both extreme voltages.
Simple example: A CMOS inverter can be (and is) used as a linear amplifier if properly biased.