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Journals / Eastern Anatolian Journal of Science / 2026 / Volume: 12 Issue: 1

New Fractional Integral Inequalities for AG-Convex and GA-Convex Functions

Sinan Aslan(AGRI IBRAHIM CECEN UNIVERSITY)0000-0001-5970-1926
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Publication Date
2026-10-18
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The presented approach provides a useful analytical technique for future investigations involving generalized convexity and fractional integral operators with nonsingular kernels.

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper, we establish several new fractional integral inequalities for arithmetic–geometrically convex (AG-convex) and geometrically–arithmetic convex (GA-convex) functions by means of the Caputo–Fabrizio fractional integral operator.
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Key Findings & Data:The obtained results unify and generalize several previously known inequalities for generalized convex functions and demonstrate the effectiveness of the Caputo–Fabrizio fractional framework in the study of integral inequalities.
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Conclusion & Impact:The presented approach provides a useful analytical technique for future investigations involving generalized convexity and fractional integral operators with nonsingular kernels.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Caputo-Fabrizio fractional integral operator · AG- convex functions · GA-convex functions

Abstract

In this paper, we establish several new fractional integral inequalities for arithmetic–geometrically convex (AG-convex) and geometrically–arithmetic convex (GA-convex) functions by means of the Caputo–Fabrizio fractional integral operator. By combining the structural properties of generalized convexity with the nonsingular exponential kernel of the Caputo–Fabrizio operator, we derive new Hermite–Hadamard-type estimates that extend a number of existing integral inequalities in the literature. Furthermore, Hölder's inequality and Young's inequality are employed to obtain refined upper bounds under suitable assumptions. The obtained results unify and generalize several previously known inequalities for generalized convex functions and demonstrate the effectiveness of the Caputo–Fabrizio fractional framework in the study of integral inequalities. The presented approach provides a useful analytical technique for future investigations involving generalized convexity and fractional integral operators with nonsingular kernels.

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Cite This Article

Aslan, S. (2026). New Fractional Integral Inequalities for AG-Convex and GA-Convex Functions. Eastern Anatolian Journal of Science, Volume: 12 Issue: 1. https://ajindex.com/articles/1475616

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