In this paper, we analyze the concept of observability in the case of conformable time-invariant linear control systems. Also, we study the Gramian observability matrix of the conformable linear system, its rank criteria, null space, and some other conditions. We also discuss some properties of conformable Laplace transform.

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We relate this article to the emerging idea of distinguishability of conformable linear hybrid time-invariant control systems. To obtain the necessary and sufficient conditions of α \alpha -distinguishability for fractional cases, we develop the Leibnitz rule for conformable derivatives. Furthermore, with the help of a study of Laplace techniques, a more simple criterion of α \alpha -distinguishability for the fractional linear system is developed.