The Hindustani language is Hindi-Urdu dialect continuum. It is derived regularly from older stages of Indo-Aryan (like Sanskrit). You have already noted the influence of Persian (which was a major one because it was the official language of the Moghul empire), Turkish (which was minor and mainly through Persian transmission), and Arabic (both through Persian transmission and directly through the influence of Islam on Hindustani, the influence is bigger for Urdu than for Hindi).
Other major influences to Hindustani are the Western languages, first Portuguese and later English. Hindi is also influenced by learned borrowings and calques from Sanskrit.