Apparent from the names of months the calendar is not just a "gift" of the "Muslim civilization". It was the Indian calendar that Akbar used and maybe made a few alterations here and there. He apparently also just designated the start point. Also note the Sri Lankan new years is right before the Bengali (13th) the Nepali just before that 12th. Did the Muslims give the gift of the Nepali and Sri Lankan calendar aswell?

Rather the calendar is reformed from the old calendar

http://webexhibits.org/calendars/calendar-indian.html

History of the Indian calendar

The history of calendars in India is a remarkably complex subject owing to the continuity of Indian civilization and to the diversity of cultural influences. In the mid-1950s, when the Calendar Reform Committee made its survey, there were about 30 calendars in use for setting religious festivals for Hindus, Buddhists, and Jainists. Some of these were also used for civil dating. These calendars were based on common principles, though they had local characteristics determined by long-established customs and the astronomical practices of local calendar makers. In addition, Muslims in India used the Islamic calendar, and the Indian government used the Gregorian calendar for administrative purposes.

Early allusions to a lunisolar calendar with intercalated months are found in the hymns from the Rig Veda, dating from the second millennium B.C.E. Literature from 1300 B.C.E. to C.E. 300, provides information of a more specific nature. A five-year lunisolar calendar coordinated solar years with synodic and sidereal lunar months.

Indian astronomy underwent a general reform in the first few centuries C.E., as advances in Babylonian and Greek astronomy became known. New astronomical constants and models for the motion of the Moon and Sun were adapted to traditional calendric practices. This was conveyed in astronomical treatises of this period known as Siddhantas, many of which have not survived. The Surya Siddhanta, which originated in the fourth century but was updated over the following centuries, influenced Indian calendrics up to and even after the calendar reform of C.E. 1957.

The author Pingree provides a survey of the development of mathematical astronomy in India. Although he does not deal explicitly with calendrics, this material is necessary for a full understanding of the history of India's calendars.

Che