If the supply is supposed to deliver relatively constant current, filtering can be done using lots of inductance, combined with a bit of resistance.
Another possibility is to use a very (impractically) large number of small-value non-electrolytic capacitors in parallel, in place of what would ordinarily be an electrolytic capacitor.
It's possible to use an op-amp with a capacitor to produce a "virtual inductor". It should be equally possible to use an op-amp with an inductor to produce a "virtual capacitor". I've never heard of anyone actually doing this, because typically, capacitors are cheaper and smaller than inductors.
I wouldn't think any of these strategies would be particularly practical; there are good reasons why power supplies have electrolytic capacitors. Electrolytic capacitors have advantages in areas of expense, size, and weight. But as a thought experiment, or an "I want to do this to prove it's possible" project, it should be possible.