In this paper, we introduce several various classes of c-almost periodic type functions and their Stepanov generalizations, where c ∈ ℂ and |c| = 1. We also consider the corresponding classes of c-almost periodic type functions depending on two variables and prove several related composition principles. Plenty of illustrative examples and applications are presented.
In this paper, we introduce the classes of $(\omega, c)$-pseudo almost periodicfunctions and $(\omega, c)$-pseudo almost automorphicfunctions. These collections include $(\omega, c)$-pseudo periodicfunctions, pseudo almost periodic functions and their automorphic analogues.We present an application to the abstract semilinear first-order Cauchy inclusions in Banach spaces.
The main aim of this paper is to indicate that the notion of semi-
c
-periodicity is equivalent with the notion of
c
-periodicity, provided that
c
is a nonzero complex number whose absolute value is not equal to 1.
The paper is a study of the (w, c) −pseudo almost periodicity in the setting of Sobolev-Schwartz distributions. We introduce the space of (w, c) −pseudo almost periodic distributions and give their principal properties. Some results about the existence of distributional (w, c) −pseudo almost periodic solutions of linear differential systems are proposed.
In this work, we introduce the notion of a (weak) proportional Caputo fractional derivative of order α∈(0,1) for a continuous (locally integrable) function u:[0,∞)→E, where E is a complex Banach space. In our definition, we do not require that the function u(·) is continuously differentiable, which enables us to consider the wellposedness of the corresponding fractional relaxation problems in a much better theoretical way. More precisely, we systematically investigate several new classes of (degenerate) fractional solution operator families connected with the use of this type of fractional derivatives, obeying the multivalued linear approach to the abstract Volterra integro-differential inclusions. The quasi-periodic properties of the proportional fractional integrals as well as the existence and uniqueness of almost periodic-type solutions for various classes of proportional Caputo fractional differential inclusions in Banach spaces are also considered.
In this paper, we introduce several various classes of c-almost periodic type functions and their Stepanov generalizations, where c ∈ C and |c| = 1. We also consider the corresponding classes of c-almost periodic type functions depending on two variables and prove several related composition principles. Plenty of illustrative examples and applications are presented.
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