On quasi-periodic properties of fractional sums and fractional differences of periodic functions

This article is devoted to the study of discrete fractional calculus; our goal is to investigate quasi-periodic properties of fractional order sums and differences of periodic functions. Using Riemann–Liouville and Caputo type definitions, we study concepts close to the well known idea of periodic function, such as asymptotically periodicity or S-asymptotically periodicity. We use basic tools of discrete fractional calculus. Boundedness of sums and differences of fractional order of a given periodic function is also investigated.