Work

Caputo-Hadamard fractional Wirtinger-type inequalities via Taylor expansion with applications to classical means

Year: 2025

Type: article

Abstract: In this paper, we explored Caputo-Hadamard fractional Wirtinger-type inequalities using Taylor's formula. The main findings were derived by utilizing Hölder's inequality to derive results for Caputo-Hadamard fractional derivatives in terms of $ \textbf{L}_{q} $ norms for $ q > 1 $. Through graphical interpretation, we confirmed the validity of the results. A flowchart summarizing the logical progression from lemma to theorem was added for clarity. Furthermore, inequalities were also derived for Hadamard fractional derivatives. Finally, we discussed the applications of Wirtinger-type inequalitie which incorporates arithmetic mean and geometric mean-type inequalities.

Source: AIMS Mathematics

DOI: 10.3934/math.2025730

Authors: Muhammad Samraiz, Humaira Javaid, Muath Awadalla, Hajer Zaway

Institutions: University of Sargodha, King Faisal University

Language: English

Topic: Mathematical Inequalities and Applications

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

Funder: King Faisal University