Q. A person who is not ill, but finds fasting hard because of his age; he does usually fast on other taaneisim. Can he avoid fasting on Tzom Gedalia since it is as is a nidche? (Gedalia was assassinated on Rosh Hashana and the taanis was pushed off to the day after, so it is less than other fast days).

A. Poskim differ as to when Gedalia was assassinated. Rabbenu Yerucham (P. 164, quoted by Beis Yosef and Beer Heitev 549: 1) maintains that indeed he was killed on Rosh Hashana and because of the day being Yom Tov it was differed to the third of Tishrei. Eben Ezrah (Zecharia 8: 19) writes that he died on the first day Rosh Hashana. Others mention that it was on the second day Rosh Hashana (Knesses Yechezkel O.H. 23). There is an opinion that he was struck on Rosh Hashana, but died from his wounds the next day (Yalkut Hagershuni quoting Divrei Shoul).
However, the Talmud (Rosh Hashana 18b), Rambam (H. Taanios 5: 2), Tur (O.H. 549), Ritvo (quoted in Biur Halocho ibid.) and most Poskim write that Gedalia died on the third day of Tishrei. Yaaros Devash (2: 1 – see also Kaf Hachaim ibid.) explains that Tzom Gedalia, gives echo to the teaching of the Mekubalim, that every day of the Yemei Teshuva represents one of the Ten Commandments and the third day stands for Lo Tirzach or do not commit murder.
Beer Heitev (ibid.) and others assert that even if we follow the opinion that he died on Rosh Hashana, since it was from the onset established as a day of fasting on the third of Tishrei, it does not qualify as as a nidche or a differed taanis. However, Nitei Gavriel (Yom Kippur 1: 2) does mention that some Poskim are lenient for the ones in need.
Horav Shlomo Miller’s Shlit’a opinion is that one should deal and address Tzom Gedalia as one does similar taaneisim, and if he is able to fast on them, he should equally do so on this taanis.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a