A Note on a Semilinear Fractional Differential Equation of Neutral Type with Infinite Delay. (26th January 2010)

• Record Type: Journal Article
• Authors: Mophou, Gisle M.; N'Guérékata, Gaston M.
• Other Names: Pankov A. Academic Editor.
• Is Part Of: Advances in difference equations. Volume 2010(2010)
• Publication Date: 2010-01-26
• Subjects: Difference equations -- Periodicals; 515.625
• DOI: 10.1155/2010/674630
• Languages: English
• ISSNs: 1687-1847

Abstract

Abstract : We deal in this paper with the mild solution for the semilinear fractional differential equation of neutral type with infinite delay:D α x ( t ) + A x ( t ) = f ( t, x t ), t ∈ [ 0, T ], x ( t ) = ϕ ( t ), t ∈ ] − ∞, 0 ], withT > 0 and0 < 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 space𝕏 by means of the Banach's fixed point theorem. This generalizes some recent results.