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

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  • Coşkun Yakar

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.

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  • Coşkun Yakar, 2010. "Fractional Differential Equations in Terms of Comparison Results and Lyapunov Stability with Initial Time Difference," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-16, February.
    • Handle: RePEc:hin:jnlaaa:762857
    DOI: 10.1155/2010/762857
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