Asymptotic Properties of Fractional Delay Differential Equations

Katja Krol

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976),

MSC 2000

34K06 Linear functional-differential equations

26A33 Fractional derivatives and integrals

34K20 Stability theory

34K25 Asymptotic theory

34D05 Asymptotic properties

34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions

Abstract
In this paper we study the asymptotic properties of d-dimensional linear fractional differential equations with time delay. First results on existence and uniqueness of solutions are presented. Then we propose necessary and sufficient conditions for asymptotic stability of equations of this type using the inverse Laplace transform method.