International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 45-48, 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
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.