Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces

Diagana, Toka

doi:10.1007/978-3-319-00849-3

Cited by 199 publications

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“…Almost periodic and asymptotically almost periodic solutions of differential equations in Banach spaces have been considered by many authors so far (for the basic information on the subject, we refer the reader to the monographs [1][2][3][4][5][6][7][8][9][10]). Concerning almost automorphic and asymptotically almost automorphic solutions of abstract differential equations, one may refer, for example, to the monographs by Diagana [4], N'Guérékata [5], and references cited therein.…”

Section: Introductionmentioning

confidence: 99%

Generalized Asymptotically Almost Periodic and Generalized Asymptotically Almost Automorphic Solutions of Abstract Multiterm Fractional Differential Inclusions

N’Guérékata

Kostić

2018

Abstract and Applied Analysis

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Section: Introductionmentioning

confidence: 99%

Generalized Asymptotically Almost Periodic and Generalized Asymptotically Almost Automorphic Solutions of Abstract Multiterm Fractional Differential Inclusions

N’Guérékata

Kostić

2018

Abstract and Applied Analysis

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“…The relative compactness of subsets in AP(I : X) has been examined by Corduneanu [23] (see also [17,Theorem 3.11]). A function f ∈ BUC(I : X) is said to be weakly almost periodic in the sense of Eberlein if and only if {f (· + s) : s ∈ I} is relatively weakly compact in X.…”

Section: Remark 23 It Is Worth Noting That Assertion (8) In Theorem mentioning

confidence: 99%

“…The notion of an asymptotically almost periodic function was introduced by Fréchet in 1941 (for more details concerning the vector-valued asymptotically almost periodic functions and asymptotically almost periodic differential equations, see, e.g., [17,18,[24][25][26][27][28][29][30]…”

Section: Asymptotically Almost Periodic Functionsmentioning

confidence: 99%

Almost periodic and asymptotically almost periodic functions: part I

Lassoued

Shah

2018

Adv Differ Equ

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In this paper, we review indispensable properties and characterizations of almost periodic functions and asymptotically almost periodic functions in Banach spaces. Special accent is put on the Stepanov generalizations of almost periodic functions and asymptotically almost periodic functions. We also recollect some basic results regarding equi-Weyl-almost periodic functions and Weyl-almost periodic functions. The class of asymptotically Weyl-almost periodic functions, introduced in this work, seems to be not considered elsewhere even in the scalar-valued case. We actually introduce eight new classes of asymptotically almost periodic functions and analyze relations between them. In order to make a picture as complete and clear as possible, several illustrating examples and counter-examples are given. It is worth noting that the topics dealt with in this paper seem to be of an intrinsic connection with the problem of existence and uniqueness of solutions of differential and difference equations, in both determinist and stochastic cases. MSC: 42A75

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“…It is well known that the class of almost periodic function was introduced by Bohr in 1925 and later generalized by many other mathematicians (for further information, the reader may consult the monographs (Diagana, 2013;N'Guérékata, 2001;Hino et al, 2002;Levitan and Zhikov, 1982)). Let I = ℝ or I = [0, ∞) and let f: I → X be continuous and let ϵ > 0.…”

Section: Almost Periodic Functions and Stepanov Almost Periodic Functmentioning

confidence: 99%

On Almost Periodic Solutions of Abstract Semilinear Fractional Inclusions with Weyl-Liouville Derivatives of Order <i>γ</i> ∈ (0, 1]

cacute¹

2017

Journal of Mathematics and Statistics

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Abstract:The main aim of this paper is to examine the existence and uniqueness of almost periodic solutions for a class of (semilinear) fractional relaxation inclusions with Stepanov almost periodic coefficients. We deal with the Weyl-Liouville fractional derivatives of order γ ∈ (0, 1], paying special attention to the analysis of semilinear differential inclusions of first order. We use the results from the theory of fractional powers of sectorial multivalued linear operators to achieve our goals, providing an interesting application to semilinear fractional Poisson heat equation in L p -spaces.

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Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces

Cited by 199 publications

References 0 publications

Generalized Asymptotically Almost Periodic and Generalized Asymptotically Almost Automorphic Solutions of Abstract Multiterm Fractional Differential Inclusions

Generalized Asymptotically Almost Periodic and Generalized Asymptotically Almost Automorphic Solutions of Abstract Multiterm Fractional Differential Inclusions

Almost periodic and asymptotically almost periodic functions: part I

On Almost Periodic Solutions of Abstract Semilinear Fractional Inclusions with Weyl-Liouville Derivatives of Order <i>γ</i> ∈ (0, 1]

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Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces

Cited by 199 publications

References 0 publications

Generalized Asymptotically Almost Periodic and Generalized Asymptotically Almost Automorphic Solutions of Abstract Multiterm Fractional Differential Inclusions

Generalized Asymptotically Almost Periodic and Generalized Asymptotically Almost Automorphic Solutions of Abstract Multiterm Fractional Differential Inclusions

Almost periodic and asymptotically almost periodic functions: part I

On Almost Periodic Solutions of Abstract Semilinear Fractional Inclusions with Weyl-Liouville Derivatives of Order <i>&gamma;</i> &isin; (0, 1]

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On Almost Periodic Solutions of Abstract Semilinear Fractional Inclusions with Weyl-Liouville Derivatives of Order <i>γ</i> ∈ (0, 1]