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

2015/07/20 by Iván Area, Area, Iván, Jorge Losada +3 · 1 citation
Mathematics · #26A33 34A08 #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical functions and polynomials #Nonlinear Differential Equations Analysis #math.CA #msc:26A33 #msc:34A08

paper · pdf · doi:10.48550/arxiv.1507.05567

15 pages, 2 figures

arxiv created 2015/07/20 · openalex publication_date 2015/07/20 · arxiv updated 2015/07/21 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

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.

Citations

• The Brezis-Nirenberg result for the fractional Laplacian

Cited by

• Hill-Type Stability Analysis of Periodic Solutions of Fractional-Order Differential Equations

Related

• On fractional derivatives and primitives of periodic functions
• The Grünwald-Letnikov fractional-order derivative with fixed memory length
• Remotely c-almost periodic type functions in \mathbb Rⁿ
• On asymptotic periodic solutions of fractional differential equations and applications
• Generalized c-almost periodic type functions in \mathbb Rⁿ