Someone Ill with a Non-Life-Threatening Illness, An Elderly Person, and a Woman who has Recently Given Birth
One who is ill (meaning when one is actually bedridden and the like, even if the illness is not life-threatening) is exempt from fasting on Tisha Be’av. When in doubt about one’s status, one should consult a prominent halachic authority. (Aches and pains, such as the common headache and the like, are not grounds to exempt one from fasting on Tisha Be’av.)

An elderly person who is weakened by fasting is considered “ill” for all intents and purposes and is exempt from fasting on Tisha Be’av; even if he has no internal illness, he must nevertheless eat on Tisha Be’av.

There is a dispute among the Poskim regarding the status of a woman who has recently given birth. Regarding a woman who has given birth within the past seven days, all opinions agree that she is exempt from fasting on Tisha Be’av. However, if she has given birth more than seven days ago but she is still within thirty days of giving birth, several Poskim are of the opinion that she must act stringently and fast on Tisha Be’av. However, Maran Rabbeinu Ovadia Yosef zt”l rules that as long as the woman is within thirty days of giving birth, she is exempt from fasting.

The same applies to a woman who, G-d-forbid, miscarries following at least forty days of pregnancy (meaning that she miscarried a fetus who was in the womb for forty days or more; these forty days are counted from the actual conception, not the way doctors count beginning from an additional two weeks later) in that she is exempt from fasting on Tisha Be’av as long as she is still within thirty days of the miscarriage.

Pregnant and Nursing Women
Although pregnant and nursing women are exempt from all other public fasts (besides for Yom Kippur), they are nevertheless obligated to fast on Tisha Be’av most years.

Nevertheless, on years during which Tisha Be’av falls out on Shabbat and the fast is postponed until Sunday, such as this year, 5775, Maran Rabbeinu Ovadia Yosef zt”l rules (in his Responsa Yabia Omer, Volume 5, Chapter 40) that pregnant and nursing women are exempt from the fast of Tisha Be’av. He proceeds to bring sources and proofs to his opinion. He writes that Hagaon Harav Yehuda Shako zt”l (one of the greatest luminaries of Jerusalem approximately sixty years ago) agreed with his ruling. Indeed, in his youth, Maran zt”l was a member of his Bet Din (rabbinical court) alongside Hagaon Harav Ezra Attia zt”l and he would discuss his halachic responsa with them in order to receive their approbation.

The modern-day Poskim disagree as to when pregnant and nursing women may begin to eat on Tisha Be’av. We have posed this question to Maran zt”l and he replied that it is preferable that such woman not completely remove themselves from the fast being observed by the rest of the Jewish nation and it is proper that they not eat until the afternoon of Sunday, the Tenth of Av, meaning past halachic midday (in Jerusalem at approximately 12:45 pm and in New York at approximately 1:01 pm). Obviously, this applies only when they do not feel any significant weakness, dehydration, and the like, for according to the letter of the law, they may eat anytime on Tisha Be’av this year, as we have explained.

Children
Children, meaning a boy who has not reached thirteen years of age and a girl who has not reached twelve years of age, are completely exempt from fasting on Tisha Be’av. The reason why children are exempt from participating in this fast is because children are exempt from all of the laws of mourning in any case. Indeed, if G-d-forbid a child loses a parent, he need not mourn at all, for the Mitzvah of educating children does not apply here (besides for the law of rending the child’s garment which does apply). Any boy who has not reached the age of thirteen or girl who has not reached the age of twelve is completely exempt from the fast and they need not even fast for several hours.