New class of conformable derivatives and applications to differential impulsive systems

Abstract

In this paper, first we introduce new definition of conformable fractional derivatives and study their algebraic properties. As application, we consider certain classes of conformable differential linear systems subject to impulsive effects and establish qualitative behavior of the nontrivial solutions such as stability, disconjugacy, nonexistence, upper bound estimation for maximum number of zeros of the nontrivial solutions and some oscillatory properties. The main tool of this establishment concerns with Lyapunov inequalities of under study fractional order linear systems.