What is this anime that was shown in Akira?
It's almost certainly an outright reference to the well-known live-action show Mito Komon.


  The title character is the historic Tokugawa Mitsukuni, former vice-shogun and retired second daimyo of the Mito Domain. In the guise of Mitsuemon, a retired crêpe merchant from Echigo, he roams the realm with two samurai retainers, fun-loving Sasaki Sukesaburō (Suke-san) and studious Atsumi Kakunoshin (Kaku-san). An episode typically starts with some injustice perpetrated by a corrupt official, wealthy merchant or gangster; the travelers arrive incognito, discover the injustice and quietly investigate it; and the episode concludes with a brawl in which the unarmed, disguised protagonists better a crowd of samurai and gangsters, culminating with the presentation of the inrō that reveals the hero's identity.


I wasn't aware there was an animated version.  Mito Komon has been around for decades (1969-2011, over 1200 episodes), like their own version of Doctor Who.

Since it's a well-known part of pop-culture, the show is often referenced or outright parodied, like in Samurai Champloo (Mugen, it'll be our little secret....).