On quasi-periodicity properties of fractional integrals and fractional\n 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

paper · pdf · doi:10.48550/arxiv.1507.05567

openalex publication_date 2015/07/20 · 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\norder integrals and derivatives of periodic functions. Considering\nRiemann-Liouville and Caputo definitions, we discuss when the fractional\nderivative and when the fractional integral of a certain class of periodic\nfunctions satisfies particular properties. We study concepts close to the well\nknown idea of periodic function, such as S-asymptotically periodic,\nasymptotically periodic or almost periodic function. Boundedness of fractional\nderivative and fractional integral of a periodic function is also studied.\n

Citations

• The Brezis-Nirenberg result for the fractional Laplacian

Cited by

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

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