Those prescriptions that were given by Rabbi Yitzchak Luria (the Arizal), for achieving atonement by fasting specific numbers of days for certain specific sins, were based on Kabbalah and were relevant only for Jews. They also only applied in earlier generations (hundreds of years ago and earlier; the AriZal lived in the 1500's C.E.), when Jews were generally physically much stronger and more able to frequently fast than they are in modern times. Nowadays, city and suburban life has become the norm for most Jews, and even farming is accomplished with the aid of labor-saving machinery.
And in any event, the purpose of those fast prescribed by the AriZal was for *atonement*, NOT for repentance. The process of *repentance* that a person is obligated to do, to abandon a sinful behavior and gain forgiveness from G-d, does not require fasting at all. As Rambam explained in Mishneh Torah,
“And what is repentance? It is when the sinner abandons his sin, removing it from his thoughts [i.e. he will from now on push out from his mind any idea to do or to imagine doing this sin], and is completely resolved not to do it again.
Consequently, he [verbally] regrets what has happened in the past [i.e. what he thought, said or did] and [verbally] accepts G-d, the Knower of secrets, as his witness that he will never return to such a sin again.
And he needs to confess verbally and state the resolutions that he made in his heart.”
AFTER a person has sincerely repented for sinning, the objective of which is for the sin to be removed and forgiven by G-d, then the subsequent "atonement" to G-d means working to reconnect one's personal bond and relationship with G-d that was spoiled by the sin that was committed. As an analogy in human terms: if you behave badly and slap your friend in the face, you will then feel badly and return to your friend and ask to be forgiven. But even though your friend accepts your regret and therefore forgives you wholeheartedly, the closeness of the relationship has been damaged. Knowing this, you will send a gift to your friend or do something extra for him that he desires, in order to restore the closeness in the relationship that you had damaged.
Rabbi Shneur Zalman of Liadi (
https://asknoah.org/essay/rabbi-shneur-zalman) explained that in our later generations, when people would get physically or emotionally compromised by excessive or repeated fasting, the Torah-based recommendation for achieving atonement (after the sincere repentance as outlined above), is by giving proper charity. The loss (sacrifice) of a person's blood and body mass through fasting is substituted by the loss (sacrifice) of the person's money through charity, which he otherwise could have used to buy his own food or supply his other needs or wants.
When done sincerely for this purpose, the giving of proper charity accomplishes atonement, because G-d desires that people should do acts of goodness and kindness, which is exceedingly important in our time - especially in order to facilitate and hasten the coming of the true Messiah, may this happen very speedily in our days!