A proof for non existence of periodic solutions in time invariant fractional order systems. (English) Zbl 1193.34006

Summary: The aim of this note is to highlight one of the basic differences between fractional order and integer order systems. It is analytically shown that a time invariant fractional order system contrary to its integer order counterpart cannot generate exactly periodic signals. As a result, a limit cycle cannot be expected in the solution of these systems. Our investigation is based on Caputo’s definition of the fractional order derivative and includes both the commensurate or incommensurate fractional order systems.


34A08 Fractional ordinary differential equations
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
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