A class of fractional dynamic systems with fuzzy order

Differentiation and integration of non-integer order have drawn increasing attention in research community. Fractional order dynamic systems have been recognized as effective tools for characterizing the real-world phenomena around and inside us. From the notion of fuzzy logic, it is natural to quest the potential of fractional dynamic systems with fuzzy orders. In this paper, for the first time, we propose the basic framework of fractional order dynamic system with fuzzy order. This basic idea is to adopt fuzzy system to characterize the differential order in a class of variable-order or constant-order fractional dynamic systems. Examples are included to illustrate the operating process.