Eur. Phys. J. Special Topics 226, 3609–3637 (2017)
https://doi.org/10.1140/epjst/e2018-00051-7

Regular Article

Stability analysis of the set of trajectories for differential equations with fractional dynamics

¹ S. P. Timoshenko Institute of Mechanics NAS of Ukraine, Nesterov str., 3, 03057, Kiev-57, Ukraine
² University of Texas at San Antonio, Department of Mathematics, San Antonio, TX 78249, USA

^a e-mail: ivanka.stamova@utsa.edu

Received: 25 July 2017
Received in final form: 26 September 2017
Published online: 25 July 2018

Abstract

In this paper we consider the problem of stability analysis of the set of trajectories for fractional differential equations under interval initial conditions. Sufficient conditions for Lyapunov-type stability and Mittag-Leffler stability are obtained based on some matrix auxiliary Lyapunov functions and a pseudo-linear representation of integral inequalities.