Dear Rabbi Maroof,
Why do Sephardic/Mizrahi Jews wear Tefillin at Minha on the Fast of Gedaliah?
Many Sephardic communities have the custom of donning Tefillin at the Minha (afternoon) service on all fast days (except, of course, Yom Kippur). This practice is mentioned by Rabbi Yosef Karo in his classic commentary, the Bet Yosef.
Three main reasons are offered for the custom. The first explanation relates to berachot (blessings). We are required to recite a minimum of one hundred blessings a day. A typical daily routine, including blessings on foods, etc., will satisfy this requirement almost "naturally". However, on fast days, the fact that we don't consume any food takes a toll on our "beracha count." Wearing Tefillin at Minha gives us the opportunity to make an additional blessing.
Another explanation of the custom is based upon the laws of Tefillin themselves. Theoretically, Tefillin should be worn all day long on weekdays. This is problematic because wearing Tefillin requires a level of purity of thought and focus that is difficult to attain, let alone to sustain for an entire day of work, school, etc. Therefore, our custom is to wear Tefillin only during the morning service since, even during Minha prayers, we tend to be quite distracted. On Fast Days, though, our abstention from food and drink brings us to a higher level of spiritual awareness. As a result, we are capable of donning Tefillin at Minha time as well.
A third explanation of the custom points to the function of Tefillin as tools that enhance our kavanah (concentration). When we have Tefillin on our arms and heads, we remain more vigilant about the direction of our thoughts and more definite in our sense of purpose. On Fast Days, we wish for our prayers to be of an especially high quality. Therefore, we wear Tefillin at Minha as well as Shaharit, to help us engage our minds even more fully and intensely in the all of the services of the day.