Possibly the most famous example of fictional physics in anime would be the Minovsky particles and Megaparticles from the Universal Century Gundam timeline. Megaparticles are easier to explain; so called because they are large for a subatomic particle, their properties are the explanation for most of the more futuristic weaponry.
Minovsky particles are more interesting because they show how committed Tomino was to justifying what he thought needed to be justified, even though he could have easily gotten by with no explanation for this. (But Tomino’s ideas of what was and wasn’t realistic weren’t always right. The Guntank, actually more realistic than walking mobile suits like the Gundam, was phased out for being “too super robot” just because Getter-3 also had treads instead of legs.)