Noted primarily for his work in opera, among other schools, Fulton studied conducting under Max Rudolf at Curtis Institute of Music and served as an assistant to him and to his successor, David Effron, coaching for the Opera Department, preparing productions and sometimes playing for the studio productions.
He debuted at the Metropolitan Opera in New York City in 1979 and remained with the company until his death.
He conducted 192 performances at the Met of over 20 operas in the Italian, French and German repertoires.
A 1982 performance he conducted of Humperdinck's Hansel and Gretel was telecast on PBS and remains available on video as a DVD.
According to his obituary, Fulton died from kidney failure while vacationing in Milan.