Is expiation incumbent upon one who made a covenant with Allah to abandon sins, then committed them without an oath, and does the ruling differ if the act lasted for minutes?

It is not permissible for a Muslim to enter pornographic websites, and if he does, he must repent. If he makes a covenant with his Lord to abandon them but then fails to fulfill his covenant, he must also repent for not fulfilling his covenant. If the wording of the covenant was "Upon me is the covenant of Allah" or "By the covenant of Allah," then he must offer expiation for a broken oath (kaffarat yameen) if he intended it as an oath or uttered it generally. However, if he said, "I covenant with Allah," some scholars do not consider expiation necessary for it.