Do my deceased brother's children have a right upon me that is obligatory, like the right of my own children, or is it from the door of benevolence?

Your brother's children have moral and material rights upon you, which differ from the rights of your own children. These rights are:

1. The right of maintaining kinship ties (Silat al-Rahim): They are the most deserving of your kinship ties, as they are your close kin (asabah), and you may inherit from them or they from you. You are also a mahram to their women.

2. The right to advice, guidance, and direction: This responsibility increases with the father's death, and the uncle's role in the lives of his brother's children is significant.

3. The right of guardianship: The full brother (paternal and maternal) is a guardian over his brother's daughters in marriage, and he is commanded to treat them kindly and choose what is best for them.

4. The right to financial support (Nafaqah): If what their father left them is insufficient, and they have no work, their financial support becomes obligatory upon you and their closest relatives, even if they are not heirs. The financial support is shared among the affluent relatives.