Fire Tripper

Time travel to feudal era. 

Both Fire Tripper & Inuyasha were created by Rumiko Takahashi. If you watched both of them, you'll see a lot of similarities. Suzuko (Fire Tripper) will kind of remind you of Kagome Higurashi (Inuyasha) given that they both are teenage girls from modern time ended up going to feudal-era Japan. Shukumaru (Fire Tripper) is not a half-demon like Inuyasha, but both of them defend the main female character, there are differences but I won't spoil them. But when you watch Fire Tripper you'll realize that's where Inuyasha got part of it's DNA from. If you wanted to know where Inuyasha's inspiration come from, then I would recommend Fire Tripper. Fire Tripper is basically Inuyasha Zero, Inuyasha: the beginning, Inuyasha: Origin. Whatever you want to call it, every Inuyasha fans should watch Fire Tripper to know where one-half of Inuyasha's origin came from. read more 

Time travelling to the same era with romance, based on manga of the same mangaka. 

Being that both were created by, Rumiko Takahashi, Fire Tripper is very much a prototype to what would later become Takaashi's magnum opus, Inuyasha.  

Both made by Rumiko Takahashi and both set in the feudal era.