(ω, c)-periodic functions and mild solutions to abstract fractional integro-differential equations

Abstract

In this paper we study a new class of functions, which we call (omega, c)-periodic functions. This collection includes periodic, anti-periodic, Bloch and unbounded functions. We prove that the set conformed by these functions is a Banach space with a suitable norm. Furthermore, we show several properties of this class of functions as the convolution invariance. We present some examples and a composition result. As an application, we establish some sufficient conditions for the existence and uniqueness of (omega, c)-periodic mild solutions to a fractional evolution equation.