  In present paper, the equivalence problem for fourth order differential
operators with one variable under general fiber-preserving transformation using
the Cartan method of equivalence is applied. Two versions of equivalence
problems are considered. First, the direct equivalence problem and second
equivalence problem is to determine the sufficient and necessary conditions on
two fourth order differential operators such that there exists a
fiber-preserving transformation mapping one to the other according to gauge
equivalence.
