Advances in Difference Equations
Volume 2010 (2010), Article ID 674630, 8 pages
doi:10.1155/2010/674630
A note on a semilinear fractional differential equation of neutral type with infinite delay
Gisle M. Mophou1
and Gaston M. N'guérékata2
1Département de Mathématiques et Informatique, Université des Antilles et de La Guyane, Campus Fouillole 97159 Pointe-à-Pitre Guadeloupe (FWI), France
2Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore, MD 21251, USA
Abstract
We deal in this paper with the mild solution for the semilinear fractional differential equation of neutral type with infinite delay: Dαx(t)+Ax(t)=f(t,xt), t∈[0,T], x(t)=ϕ(t), t∈]−∞,0], with T>0 and 0<α<1. We prove the existence (and uniqueness) of solutions, assuming that −A is a linear closed operator which generates an analytic semigroup (T(t))t≥0 on a Banach space 𝕏 by means of the Banach's fixed point theorem. This generalizes some recent results.