  Let $k$ be a complete discretely valued field of equal characteristic $p > 0$
with possibly imperfect residue field and let $G_k$ be its Galois group. We
prove that the conductors computed by the arithmetic ramification filtrations
on $G_k$ coincide with the differential Artin conductors and Swan conductors of
Galois representations of $G_k$. As a consequence, we give a Hasse-Arf theorem
for arithmetic ramification filtrations in this case. As applications, we
obtain a Hasse-Arf theorem for finite flat group schemes; we also give a
comparison theorem between the differential Artin conductors and Borger's
conductors.
