Wirtinger-type inequalities for Caputo fractional derivatives via Taylor's formula

Erden S., SARIKAYA M. Z., Ozdemir B. G., UYANIK N.

JOURNAL OF INEQUALITIES AND APPLICATIONS, vol.2024, no.1, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2024 Issue: 1
  • Publication Date: 2024
  • Doi Number: 10.1186/s13660-024-03194-2
  • Journal Name: JOURNAL OF INEQUALITIES AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Anadolu University Affiliated: Yes

Abstract

In this study, we firstly derive a Wirtinger-type result, which gives the connection in between the integral of square of a function and the integral of square of its Caputo fractional derivatives with the help of left-sided and right-sided fractional Taylor's Formulas. Afterward, we provide a more general inequality involving Caputo fractional derivatives for L-r norm with r>1 via Holder's inequality. Also, similar inequalities for Riemann-Liouville fractional derivatives are presented by means of a relation between Caputo fractional derivatives and Riemann-Liouville fractional derivatives.