Better Refinements of Fractional Inequalities through Harmonically Fuzzy Convexity and its Validation

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DOI: https://doi.org/10.28924/2291-8639-24-2026-207
Published: Jul 6, 2026
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Muhammad Haseeb, Rana Safdar Ali, Jamal Salah, Aseel Smerat, Muhammad Imran Hafeez, Better Refinements of Fractional Inequalities through Harmonically Fuzzy Convexity and its Validation, Int. J. Anal. Appl., 24 (2026), 207.

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Muhammad Haseeb, Rana Safdar Ali, Jamal Salah, Aseel Smerat, Muhammad Imran Hafeez

Abstract

There is a very close relation between convexity and generalized fractional operators (GFO) to improving the fractional inequalities. In this article, we describe the new form of fractional operators, named generalized proportional fuzzy fractional operators (GPFFO), and also discuss the refinements of well-known inequalities. We derive a modified version of Hermite-Hadamard-type inequalities and their refinements by utilizing the GPFFO with harmonically fuzzy convexity. Moreover, we discuss the numerical computations of our main results that show the existence of analytical and numerical behaviors. This type of validation represents the strength of our results. These new results and their numerical validations have a great contribution in the field of computational of inequalities.

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