  This paper is devoted to the study of quasi-periodic properties of fractional
order integrals and derivatives of periodic functions. Considering
Riemann-Liouville and Caputo definitions, we discuss when the fractional
derivative and when the fractional integral of a certain class of periodic
functions satisfies particular properties. We study concepts close to the well
known idea of periodic function, such as S-asymptotically periodic,
asymptotically periodic or almost periodic function. Boundedness of fractional
derivative and fractional integral of a periodic function is also studied.
