Fractional Differential Equations in Terms of Comparison Results and Lyapunov Stability with Initial Time Difference

The qualitative behavior of a perturbed fractional-order differential equation with Caputo's derivative that differs in initial position and initial time with respect to the unperturbed fractional-order differential equation with Caputo's derivative has been investigated. We compare the cl...

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Bibliographic Details
Main Author: Coşkun Yakar
Format: Article
Language:English
Published: Wiley 2010-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2010/762857
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Summary:The qualitative behavior of a perturbed fractional-order differential equation with Caputo's derivative that differs in initial position and initial time with respect to the unperturbed fractional-order differential equation with Caputo's derivative has been investigated. We compare the classical notion of stability to the notion of initial time difference stability for fractional-order differential equations in Caputo's sense. We present a comparison result which again gives the null solution a central role in the comparison fractional-order differential equation when establishing initial time difference stability of the perturbed fractional-order differential equation with respect to the unperturbed fractional-order differential equation.
ISSN:1085-3375
1687-0409