Praise be to Allah.
It is not permissible for a person to delay making up the missed Ramadaan fasts that he owed until the next Ramadaan begins with no excuse. If he does that then he has committed a sin. The scholars differed as to whether he has to offer expiation as well as make them up because of this delay or not.
Our advice to the sister who asked this question is to strive to make up the fasts that she owes with no delay, so that she does not burden herself and it then becomes difficult for her to make them up.
With regard to the issue of expiation, we have already discussed the scholarly differences of opinion concerning this matter in questions no 26865 and 21710.
From the two questions mentioned above, you may know that you do not have to offer expiation as well as making up the fasts, according to the more correct view, rather what you have to do is to repent to Allaah and resolve not to do such a thing again. If you offer expiation as well as making up the missed fasts in order to be on the safe side, there is nothing wrong with that. The expiation consists of feeding one poor person for each day.
See also question no. 43268.