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Zbl 1196.34010
Yakar, Coşkun
Fractional differential equations in terms of comparison results and Lyapunov stability with initial time difference. (English)
[J] Abstr. Appl. Anal. 2010, Article ID 762857, 16 p. (2010). ISSN 1085-3375; ISSN 1687-0409/e

The paper considers how Lyapunov stability concepts can be applied to fractional differential equations of Riemann-Liouville or Caputo type. Following a review which explains why this idea is not straightforward, the author discusses basic theory on existence and uniqueness. The concepts of ITD-stability and Lyapunov-like functions are introduced and shown to provide a useful way of understanding classical fractional stability. The paper concludes by describing some comparison results and showing how the various definitions of stability are inter-related.
[Neville Ford (Chester)]

MSC 2000:: *34A08
34D20 Lyapunov stability of ODE

Keywords: Lyapunov stability; fractional differential equations; Riemann-Liouville derivatives; Caputo derivatives; initial time difference

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