Commutativity of linear time‐varying fractional‐order systems

Abstract In this abstract, we discuss some of the key results and techniques related to the commutativity of fractional‐order LTVSs, including the use of linearity, time‐varying behavior, fractional‐order dynamics, and commutative conditions. These conditions must be satisfied in order for commutativity to hold for these systems. However, the commutativity of fractional‐order LTVSs has not been widely explored. In this paper, we explore the properties of these systems and their ability to commute. Through a simulation and mathematical analysis, we demonstrate that these systems exhibit commutativity under certain conditions. The findings and results are presented for the first time since it is not present yet in the literature and have unlimited applications for the design and control of fractional‐order systems in practical applications.