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<p>New ways for comparing and bounding strongly <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13660_2025_3266_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mo stretchy="false">(</mo> <mi>s</mi> <mo>,</mo> <mi>m</mi> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$(s,m)$</EquationSource> </InlineEquation>-convex functions using Caputo fractional derivatives and Caputo-Fabrizio integral operators are explored. These operators generalize some classic inequalities of Hermite-Hadamard for functions with strongly <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13660_2025_3266_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mo stretchy="false">(</mo> <mi>s</mi> <mo>,</mo> <mi>m</mi> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$(s,m)$</EquationSource> </InlineEquation>-convex derivatives. The findings are also applied to special functions and means involving the digamma function. Additionally, we relate our findings to applications in biomedicine, engineering, robotics, the automotive industry, and electronics.</p>

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A study of Hermite-Hadamard inequalities via Caputo-Fabrizio fractional integral operators using strongly \((s, m)\)-convex functions in the second sense

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月13日

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  • Jie Li,
  • Yong Lin,
  • Serap Özcan,
  • Muhammad Shoaib Saleem,
  • Ahsan Fareed Shah

摘要

New ways for comparing and bounding strongly ( s , m ) $(s,m)$ -convex functions using Caputo fractional derivatives and Caputo-Fabrizio integral operators are explored. These operators generalize some classic inequalities of Hermite-Hadamard for functions with strongly ( s , m ) $(s,m)$ -convex derivatives. The findings are also applied to special functions and means involving the digamma function. Additionally, we relate our findings to applications in biomedicine, engineering, robotics, the automotive industry, and electronics.