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Yakar, Coşkun

Fractional differential equations in terms of comparison results and Lyapunov stability with initial time difference. (English) Zbl 1196.34010

Abstr. Appl. Anal. 2010, Article ID 762857, 16 p. (2010).
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.
Reviewer: Neville Ford (Chester)

Cited in 10 Documents

MSC:

34A08 Fractional ordinary differential equations
34D20 Stability of solutions to ordinary differential equations

Keywords:

Lyapunov stability; fractional differential equations; Riemann-Liouville derivatives; Caputo derivatives; initial time difference
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\textit{C. Yakar}, Abstr. Appl. Anal. 2010, Article ID 762857, 16 p. (2010; Zbl 1196.34010)
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References:

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[13] C. Yakar, “Strict stability criteria of perturbed systems with respect to unperturbed systems in terms of initial time difference,” in Complex Analysis and Potential Theory, pp. 239-248, World Scientific, Hackensack, NJ, USA, 2007. · Zbl 1159.34040
[14] C. Yakar and M. D. Shaw, “A comparison result and Lyapunov stability criteria with initial time difference,” Dynamics of Continuous, Discrete & Impulsive Systems. Series A, vol. 12, no. 6, pp. 731-737, 2005. · Zbl 1172.34323
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