In this talk, we explain the Azumaya algebra structure of the sheaf of log differential operators of higher level in prime characteristic. We also discuss about a splitting module of it under a certain liftability assumption modulo $p^{2}$. As a consequence, we obtain a Simpson type equivalence of categories in positive characteristic. Our result can be regarded as a generalization of the result of Ogus-Vologodsky and Gros-Le Stum-Quiros to the case of log schemes and that of Schepler to the case of higher level.