Dear Hadi,
Dear Reader,
Thank you for your question.
Allah SWT knows that although we may have the best of intentions, we sometimes fall short, even when we make promises to Him. Out of His mercy, He has explicitly provided a way for us to atone for such broken promises.
In Islam, this atonement for breaking an oath is called kaffarat al-yamin (“expiation for an oath”). The specifications for how to fulfill this expiation are mentioned in the Quran in Sura Al-Ma’ida (5:89):
God will not take you to task for oaths which you may have uttered without thought, but He will take you to task for oaths which you have sworn in earnest. Thus, the breaking of an oath must be atoned for by feeding ten needy persons with more or less the same food as you are wont to give to your own families, or by clothing them, or by freeing a human being from bondage; and he who has not the wherewithal shall fast for three days [instead]. This shall be the atonement for your oaths whenever you have sworn [and broken them]. But be mindful of your oaths! Thus, God makes clear unto you His messages, so that you might have cause to be grateful. (Muhammad Asad translation)
Please note that the allowance to fast for three days is only in the event that the individual is unable to fulfill one of the previously mentioned options (feeding ten needly people, clothing ten needy people, or freeing someone who is enslaved).
We hope this answers your question.
In peace.