Is expiation obligatory upon one who swore not to show his brother a certain thing on his mobile phone, and then the brother tried to see it and claimed he caught a glimpse of it?

If you swore an oath to your brother that he would not see something, and then he saw it, you have broken your oath, unless your intention was that he should not see it in a specific way, or that you would not deliberately show it to him. For an oath is determined by your intention. If you had no specific intention, then expiation is incumbent upon you, which is feeding ten poor persons, or clothing them, or emancipating a slave. If you are unable to do that, then fasting for three days. This applies if you intended the oath; but if the oath was due to obsessive whispers (waswasa), then it holds no weight.