(N, Q)-periodic functions and applications to fractional difference equations

Abstract

This study is concerned with a new class of functions called (N,Q)-periodic functions with applications to Weyllike fractional difference equations. Firstly we introduce a new notion called (N,Q)-periodic function as generalizations of (N,?)-periodic sequence and Q-affine periodic sequence. Then we establish the completeness, composition and convolution of (N,Q)-periodic functions in abstract spaces. Thirdly we apply the properties of (N,Q)-periodic functions to consider the existence of (N,Q)-periodic mild solutions for a class of Weyl-like fractional difference equations. Finally some examples are given to illustrate our results.