Abstract and Applied Analysis
Volume 2010 (2010), Article ID 762857, 16 pages
doi:10.1155/2010/762857

Fractional differential equations in terms of comparison results and Lyapunov stability with initial time difference

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.