Weighted pseudo almost automorphic functions and applications to abstract differential equations

Review and Study of Some Doubly-Weighted Pseudo-almost Periodic Solutions of Some Partial Evolution Equations

“…[11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] of the most attractive topics in qualitative theory of differential equations due to possible applications. Some contributions on weighted pseudo-almost periodic functions, their extensions, and their applications to differential equations have recently been made, among them are for instance [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] and the references therein. However, the problem which consists of the existence of doubly-weighted pseudo-almost periodic(mild) solutions to evolution equations in the form (1.1) is quite new and untreated and thus constitutes one of the main motivations of the theme.…”

Stepanov-like weighted pseudo almost automorphic solutions to fractional order abstract integro-differential equations

“…These functions are further generalized by Blot et al [6] and was named weighted pseudo almost automorphic. The authors in [6] have proved very important properties of these functions including composition theorem and completeness property. The study of weighted pseudo almost automorphic solutions of various kind of differential equations are very new and an attractive area of research.…”

“…Pseudo almost automorphic functions are natural generalization of almost automorphic functions and introduced by Liang et al [29]. These functions are further generalized by Blot et al [6] and was named weighted pseudo almost automorphic. The authors in [6] have proved very important properties of these functions including composition theorem and completeness property.…”

Translation invariance and related properties of μ-pseudo almost automorphic (periodic) functions with application

“…Then these concepts are generalized in various ways, say, pseudo almost periodicity (Zhang [1][2][3]), weighted pseudo almost periodicity (Diagana [4,5]), pseudo almost automorphy (Liang, Xiao and Zhang [6,7]), weighted pseudo almost automorphy (Blot et al [8]), etc. These concepts have been widely used in the investigation of ordinary differential equations, partial differential equations, functional differential equations and fractional differential equations.…”