Analyzing Observability of Fractional Dynamical Systems Employing ψ-Caputo Fractional Derivative

Abstract

In this present article, we inquire into the observability of linear and nonlinear fractional dynamical systems in terms of ψ-Caputo fractional derivative. The observability Grammian matrix, which is positive definite and expressed by the Mittag-Leffler functions, is used to obtain the necessary and sufficient conditions of observability of linear fractional dynamical systems, and Banach’s fixed point theorem is used to get the sufficient conditions for the observability of nonlinear fractional systems. Three numerical examples are given to demonstrate the applicability of theoretical results for linear and nonlinear cases.