On quasi-periodicity properties of fractional integrals and fractional derivatives of periodic functions

摘要

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