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<p>This article examines famous fractional Hermite–Hadamard integral inequalities through the applications of fractional Caputo derivatives and extended convex functions. We develop modifications involving two known classical fractional extended versions of the Hermite–Hadamard type inequalities for the convex function extensions. We also obtain the refinements of some inequalities like Fejér–Hadamard, trapezoidal, and midpoint type for two extended convex functions by applying the Caputo fractional derivative identities. The presented results yield both generalizations and improvements upon previously established inequalities.</p>

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Refinements of some fractional integral inequalities involving extended convex functions and fractional Caputo derivatives

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月3日

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  • Muhammad Imran,
  • Shahid Mubeen,
  • Aziz Khan,
  • Thabet Abdeljawad

摘要

This article examines famous fractional Hermite–Hadamard integral inequalities through the applications of fractional Caputo derivatives and extended convex functions. We develop modifications involving two known classical fractional extended versions of the Hermite–Hadamard type inequalities for the convex function extensions. We also obtain the refinements of some inequalities like Fejér–Hadamard, trapezoidal, and midpoint type for two extended convex functions by applying the Caputo fractional derivative identities. The presented results yield both generalizations and improvements upon previously established inequalities.