Answer: First let me tell you that the terms
Jihād i Akbar and Jihād i Asghar are supposedly attributed to the Prophet (sws).
However, this attribution does not have a sound basis. The chain of
narrators of this narrative is very weak. Authorities of Hadīth like Ibn
Hajr, Ibn Taymiyyah and Al-Bānī have convincingly challenged the
authenticity of this narrative.
So one can safely conclude that there is no such thing as a greater Jihād or
a lesser one.
It needs to be appreciated that the word
Jihād is used in the Qur’ān to connote striving in the way of Allah. One
particular form of such a struggle is that in which one might have to fight
for Allah’s cause. This is also termed as ‘Qitāl’. In other words, striving
in the way of Allah in whatever form one is able to in accordance with the
needs that arise is what is required from a believer. Whether striving in
His way in a particular form is more superior than some other one has not
been indicated in any authentic source.