International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 47, Pages 2503-2507
doi:10.1155/S0161171204312366

Lyapunov stability solutions of fractional integrodifferential equations

Shaher Momani1 and Samir Hadid2

1Department of Mathematics, Faculty of Science, Mutah University, P.O. Box 7, Al-Karak, Jordan
2Department of Mathematics and Science, Faculty of Education and Basic Science, Ajman University of Science and Technology Network, P.O. Box 346, Ajman, United Arab Emirates

Received 28 December 2003

Copyright © 2004 Shaher Momani and Samir Hadid. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Lyapunov stability and asymptotic stability conditions for the solutions of the fractional integrodiffrential equations x(α)(t)=f(t,x(t))+∫t0tk(t,s,x(s))ds, 0<α≤1, with the initial condition x(α−1)(t0)=x0, have been investigated. Our methods are applications of Gronwall's lemma and Schwartz inequality.