How can one make up for missed prayers and fasting without remembering the date of their interruption, and how does one offer sincere repentance in this situation?

Neglecting prayer and fasting are among the major sins. The one who commits them must offer sincere repentance by abandoning them, regretting them, and resolving never to return to them. The majority of scholars hold that one must make up for missed prayers and days of fasting. If a person is unaware of the number of missed obligations, they should investigate and make up what they believe, to the best of their judgment, will absolve them.