Work

Fractal-fractional estimations of Bullen-type inequalities with applications

Year: 2024

Type: article

Abstract: The study of inequalities inside fractal domains has been stimulated by the growing interest in fractional calculus for the applied and mathematical sciences. This work uses extended fractional integrals in fractal domains to prove new Bullen-type inequalities for differentiable convex functions. By showing how these operators and inequalities can convert classical inequalities into fractal sets, it fills a vacuum in the literature on fractal-fractional integral inequalities. Using extended fractional integral operators, we derive new fractal-fractional estimates and Bullen-type inequalities, accompanied by thorough mathematical derivations and graphical validations. We show optimal results derived from new Bullen-type inequalities for fractal domains. We confirm our results with mathematical examples and graphs, improving models for complicated problems in fractal contexts. In particular, our findings have important ramifications for special means on fractal sets, probability density functions, and quadrature formulas, as well as for future study and applications.

Source: Ain Shams Engineering Journal

DOI: 10.1016/j.asej.2024.103096

Authors: Saad Ihsan Butt, Muhammad Umar Yasin, Sanja Tipurić-Spužević, Bandar Bin-Mohsin

Institutions: COMSATS University Islamabad, University of Split, King Saud University

Language: English

Topic: Mathematical Inequalities and Applications

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $860

Funder: King Saud University