Existence results for neutral integro-differential equations with unbounded delay

Existence of S-asymptotically ω-periodic solutions to abstract integro-differential equations

“…We note that conditions (P1)-(P4) have been previously considered in the literature. We refer the reader to [3][4][5][6]8,16] for details about this aspect related to the existence of the resolvent operator.…”

“…We next collect some properties established in [4] which will be needed to establish the results of this paper. In what follows we denote rðGÞ ¼ C n XðGÞ, and we define x G ¼ supfReðkÞ : k 2 rðGÞg.…”

Comparison of Adomian Decomposition and Taylor Expansion Methods for the Solutions of Fractional Integro-Differential Equations

“…The existence and uniqueness of solutions to fractional differential equations have been investigated [2,7,9,14]. In addition, when , Eq(1.1) reduces to linear integro-differential equation and the numerical methods for this equation have been extensively studied by many authors [8,12,15]. There are many methods for seeking approximate solutions such as collocation method, the fractional differential transform method, Legendre wavelet method, Taylor expansion method and Adomian decomposition method, See ([1, 4,5,10,13]).…”

Global Existence for Volterra-Fredholm Type Functional Impulsive Integrodifferential Equations

“…Also in [3], the authors studied second order impulsive functional differential inclusions by using Schaefer's theorem combined with a selection of theorem of Bressan and Colombo for lower semicontinuous multivalued operators with decomposable values. For recent results on local and global existence for ordinary, functional or neutral integrodifferential equations see [8,16,18,19,21,[25][26][27][28][29][30][31][32][33][34].…”