IJPAM: Volume 5, No. 1 (2003)

NORM CONTINUITY FOR A FUNCTIONAL
DIFFERENTIAL EQUATION WITH
FRACTIONAL POWER

Miklavz Mastinšek
EPF-University of Maribor
Razlagova 14
2000 Maribor, SLOVENIA
e-mail: mastinsek@uni-mb.si


Abstract.A functional differential equation $ du/dt = - Au(t)+$
$bA^{\alpha}u(t)+(a*Au)(t)$ is studied, where $-A$ is the infinitesimal generator of a bounded analytic semigroup in Hilbert space $X$, $A^{\alpha}$ is the fractional power of $A$ and the convolution term contains a square integrable real function $a$. Eventual norm continuity is obtained for $0\le \alpha <1$.

Received: December 28, 2002

AMS Subject Classification: 34K30, 47D06

Key Words and Phrases: functional differential equations, norm continuity

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2003
Volume: 5
Issue: 1