Level 55
@udit your question is not clear for me, but
If you want to compare today's date with the start_date of the task - for sure you can do it with Carbon. like
(assuming start_date casted as date, so, is Carbon instance)
for day of week
today()->dayOfWeek == $task->start_date->dayOfWeek
or
today()->dayOfWeekIso == $task->start_date->dayOfWeekIso
for day of month
today()->day == $task->start_date->day