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arXiv · 1507.05567

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

Iván Area·Jorge Losada·Juan J. Nieto
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Abstract

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.

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Iván Area, Jorge Losada, Juan J. Nieto. 2015-07-20. On quasi-periodicity properties of fractional integrals and fractional derivatives of periodic functions. https://arxiv.org/abs/1507.05567

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