Wirtinger-type inequalities for Caputo fractional derivatives via Taylor's formula
JOURNAL OF INEQUALITIES AND APPLICATIONS, vol.2024, no.1, 2024 (SCI-Expanded, Scopus)
- 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.