Work

On Generalized Wirtinger Inequalities for (k,ψ)-Caputo Fractional Derivatives and Applications

Year: 2025

Type: article

Abstract: The primary aim of this study is to establish new Wirtinger-type inequalities involving fractional derivatives, which are essential tools in analysis and applied mathematics. We derive generalized Wirtinger-type inequalities incorporating the (k,ψ)-Caputo fractional derivatives using Taylor’s expansion. The inequalities are derived in Lp spaces (p>1) through Hölder’s inequality. A detailed analytical discussion is provided to further examine the derived inequalities. The theoretical findings are validated through numerical examples and graphical representations. Furthermore, the novelty and applicability of the proposed technique are demonstrated through the applications of the resulting inequalities to derive new results related to the arithmetic–geometric mean inequality.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract9110678

Authors: Muhammad Samraiz, Humaira Javaid, Ishtiaq Ali

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: $3,258

Funder: King Faisal University