I have never used an online service via my phone, whether it is purchasing a product or booking a ticket. I always use the laptop only. A larger screen may reduce possible errors, especially typos and accidental clicks. I would also advise you not to save passwords on any device, be it Gmail or IRCTC, or anything else.
In case you are having problems, check via search engines if there is a problem with the website. You may come across a newsfeed or a general alert by the organization itself about the server/outage problem for a few hours or for that particular day. You could also clear cache and cookies regularly. That has sometimes helped me when I am unable to log in somewhere and there is slow loading of the pages.
When you make a commitment, you create hope. When you keep a commitment you create trust! ~ John C. Maxwell