The Chen-Marchaud fractional integro-differentiation in the variable exponent Lebesgue spaces

Humberto Rafeiro, Makhmadiyor Yakhshiboev

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

After recalling some definitions regarding the Chen fractional integro-differentiation and discussing the pro et contra of various ways of truncation related to Chen fractional differentiation, we show that, within the framework of weighted Lebesgue spaces with variable exponent, the Chen-Marchaud fractional derivative is the left inverse operator for the Chen fractional integral operator.

Original languageEnglish
Pages (from-to)343-360
Number of pages18
JournalFractional Calculus and Applied Analysis
Volume14
Issue number3
DOIs
Publication statusPublished - Sep 2011
Externally publishedYes

Keywords

  • Chen fractional integration
  • Marchaud fractional derivative
  • Riesz potentials
  • fractional integrals
  • variable exponent spaces

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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