Existence of pseudo-almost automorphic solutions to some abstract differential equations with -pseudo-almost automorphic coefficients

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

“…DEFINITION 2.5 [19] The space S p AA(R, X) of Stepanov-like almost automorphic functions (or S p -almost automorphic functions) consists of all f ∈ BS p (R, X) such that f b ∈ AA(R, L p ([0, 1], X)).…”

“…is said to be S p -almost automorphic in t ∈ R uniformly for u ∈ Y if for every sequence of real numbers (s n ) n∈N , there exist a subsequence (τ n ) n∈N and a function g : Fractional order abstract integro-differential equations DEFINITION 2.7 [19] A function f ∈ BS p (R, X) is called Stepnaov-like pseudo almost automorphic (or S p -pseudo almost automorphic) if it can be decomposed as f = g + φ, where g b ∈ AA(R, L p ([0, 1], X)) and φ b ∈ P AA 0 (R, L p ([0, 1], X)). Denote by S p P AA(R, X) the collection of such functions.…”

“…From [19], we know that the space S p P AA(R, X) is a Banach space equipped with the norm · S p . If f ∈ P AA(R, X), then f ∈ S p P AA(R, X) for each 1 ≤ p < ∞, in other words, P AA(R, X) ⊂ S p P AA(R, X).…”

Existence of Pseudo-Almost Automorphic Mild Solutions to Some Nonautonomous Partial Evolution Equations

“…Such a concept, since its introduction in the literature, has recently generated several developments; see, for example, [8][9][10][11][12] . The question which consists of the existence of pseudo-almost automorphic solutions to abstract partial evolution equations has been made; see for instance 10,11,13 .…”

Stepanov-like pseudo almost automorphic solution to a parabolic evolution equation

“…The existence and uniqueness of (pseudo) almost automorphic type solution has been one of the most attracting topics in the context of various kinds of abstract differential equations [ Pseudo almost automorphic (PAA) X i a o et al [9,10] Stepanov-like almost automorphic (S p AA) N ' G u é r é k a t a a n d P a n k o v [ 11] Weighted pseudo almost automorphic (WPAA) B l o t et al [12] Stepanov-like pseudo almost automorphic (S p PAA) D i a g a n a [ 13] Weighted Stepanov-like pseudo almost automorphic (S p WPAA) Xia and Fan [14] Figure 1 Relationship between recently developed almost automorphy, where '→' denotes subset relation '⊂' , AA is short for almost automorphic functions.…”