Question

how did the Mughal Empire established in India

Answer 1

when babur fight with Ibrahim lodi..

The Mughal Empire was founded by Babur (reigned 1526–1530), 

Answer 2

hey, here is your answer
The mughal empire was founded by Babur (resigned 1526-1530)a central Asian from the Turco) mongol conquerer Timur (The founder of the Timur empire) on his father 'S side and form chagati, the second of the mongol ruler Genghis Khan on his mother 'S side.
hope it will help you