In the Hellsing anime/manga, Abraham Van Hellsing's life mostly follows that of the novel, up until the face off with Dracula, where the story deviates, and rather than destroying him, he went through a great deal of research and through some means, turned him into a family servant, redubbing him Alucard.
Abraham Van Hellsing founded the Hellsing organization, which devoted resources to slaying vampires in England. The organization was eventually inherited by Sir Integra Fairbrook Wingates Hellsing.