Abstract and Applied Analysis

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

Coşkun Yakar

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Abstract

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.

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 762857, 16 pages.

Dates
First available in Project Euclid: 2 March 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1267538590

Digital Object Identifier
doi:10.1155/2010/762857

Mathematical Reviews number (MathSciNet)
MR2595165

Zentralblatt MATH identifier
1196.34010

Citation

Yakar, Coşkun. Fractional Differential Equations in Terms of Comparison Results and Lyapunov Stability with Initial Time Difference. Abstr. Appl. Anal. 2010 (2010), Article ID 762857, 16 pages. doi:10.1155/2010/762857. https://projecteuclid.org/euclid.aaa/1267538590


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