Gajanan, the following two articles will get you started. I'm sure you will find answer to your questions there (and even much more).

http://www.sciencedirect.com/science/article/pii/S0303243403000230

http://www.sciencedirect.com/science/article/pii/S0303243407000335

Urban sprawl can be studied using a simple multi temporal change detection method or through other sophisticated methods which are well documented in literature. I've attached some more links for some inspiration. You may also want to use Google Earth's (GE) historical time slider tool for a preliminary analysis. With GE's time slider you can get a quick feel of what urban sprawl looks like. GE mostly uses Landsat and other high resolution satellite imagery. I've added a screenshot of Bangalore city and adjoining areas from GE as it looks like in 1984 and 2016.

https://www.youtube.com/watch?v=ZVML0Iro3oY

https://pubs.usgs.gov/circ/2004/circ1252/

Hi

Here is a case study about urban sprawl.

Hope this can help you.

http://giswin.geo.tsukuba.ac.jp/sis/jikken/2016/05.pdf

I suggest you to read this paper, which exactly discusses the use of time-series Landsat images to assess urban sprawl, using open source software: Article A SMAP Supervised Classification of Landsat Images for Urban...