Much like its Western counterpart, Hindustani Classical has a 12-note scale with half-step gaps between each note; this scale encompasses an octave. However, unlike Western Classical, this scale could start on any note, and doesn't need to adhere to any specific one.
The distribution of the Scale is as such with Sa being the chosen starting note:
An interesting thing to note here is the distribution of Flats and Sharps. Unlike Western, there is only one naming convention for notes. For instance, one may not call Ma-Teevra Pa-Komal.
Delving deeper, one may note that it's impossible to truly put into notation the intricacies which make Hindustani unique. Hindustani is a style that historically was passed down through hearing between teachers(gurus and gurvis) and students. Hence, a system for writing never really developed for it.
Another reason for a lack of writing systems for Hindustani Classical could be pinned to the format of alankars. These alankars often involve movements between notes to be so intricate, it's impossible to completely represent such in writing.