First thing, take a look at JavaScript date formats and convert your input date accordingly, then you shoud take a look to the methods available in JavaScript for date manipulation (no external library required). It's pretty easy to do something like this:

var dateUTC = new Date(yourInputDateInASuitableFormat);

var dateUTC = dateUTC.getTime() 

var dateIST = new Date(dateUTC);

//date shifting for IST timezone (+5 hours and 30 minutes)

dateIST.setHours(dateIST.getHours() + 5); 

dateIST.setMinutes(dateIST.getMinutes() + 30);