Analytical stability bound for a class of delayed fractional-order dynamic systems. (English) Zbl 1020.34064

Chen, Yangquan; Moore, Kevin L.

Nonlinear Dyn. 29, No. 1-4, 191-200 (2002).

This paper looks at the combination of two important approaches to the generalisation of ordinary differential equations in mathematical models: namely the use of fractional orders of derivatives and the incorporation of delays. Following some review material, the authors go on to consider the vexed question of stability (known to present challenges in analysis of delay differential equations). They present an analytic stability bound and give some examples.

Reviewer: Neville Ford (Chester)

MSC:

34K20	Stability theory of functional-differential equations
34D05	Asymptotic properties of solutions to ordinary differential equations
37C75	Stability theory for smooth dynamical systems
34A25	Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.

Keywords:

stability; fractional differential equation; delay; delayed fractional-order dynamic systems

Software:

CRONE