On quasi-periodicity properties of fractional integrals and fractional derivatives of periodic functions. Issue 1 (2nd January 2016)

• Record Type: Journal Article
• Authors: Area, I.; Losada, J.; Nieto, J.J.
• Is Part Of: Integral transforms and special functions. Volume 27:Issue 1(2016)
• Page Start: 1
• Page End: 16
• Publication Date: 2016-01-02
• Subjects: fractional calculus -- periodic function -- S-asymptotically periodic function -- asymptotically periodic function -- almost periodic function; Primary: 26A33 -- Secondary: 34A08; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2015.1087400
• Languages: English
• ISSNs: 1065-2469

Abstract

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.