About the convergence type of improper integrals defining fractional derivatives | Zendy

Britt Kalam | Zendy; Gennadi Vainikko | Zendy

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About the convergence type of improper integrals defining fractional derivatives

Author(s) -

Britt Kalam,

Gennadi Vainikko

Publication year - 2019

Publication title -

acta et commentationes universitatis tartuensis de mathematica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.276

H-Index - 6

eISSN - 2228-4699

pISSN - 1406-2283

DOI - 10.12697/acutm.2019.23.10

Subject(s) - pointwise convergence , differentiable function , convergence (economics) , mathematics , pointwise , class (philosophy) , type (biology) , order (exchange) , convergence tests , fractional calculus , pure mathematics , mathematical analysis , rate of convergence , computer science , network topology , ecology , channel (broadcasting) , computer network , finance , artificial intelligence , economics , biology , economic growth , operating system

This article continues the analysis of the class of fractionally differentiable functions. We complete the main result of [4] that characterises the class of fractionally differentiable functions in terms of the pointwise convergence of certain improper integrals containing these functions. Our aim is to present an example, which shows that in order to obtain all fractionally differentiable functions, one may not replace the conditional convergence of those integrals by their absolute convergence.

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