fractional-order derivative

A Frequency criterion for analysis of stability of systems with fractional-order derivatives

Based on an analysis of the influence of the roots of a characteristic polynomial on the increment of the argument of the frequency characteristic of the system, the frequency criterion of stability of a system with fractional-order derivatives has been suggested.  The boundaries of the zone of location of the roots of the characteristic polynomial of a stable system have been determined in a complex plane when the index $\alpha$ of the basis of the characteristic polynomial changes.