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<p>We propose a new method for the investigation of integral identities according to tempered fractional operators. In addition, we prove the midpoint-type and trapezoid-type inequalities by using twice-differentiable convex functions associated with tempered fractional integral operators. We use the well-known Hölder inequality and the power-mean inequality in order to obtain inequalities of these types. The resulting Hermite–Hadamard-type inequalities are generalizations of some investigations in this field, involving Riemann–Liouville fractional integrals.</p>

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Hermite–Hadamard-Type Inequalities Arising from Tempered Fractional Integrals Including Twice-Differentiable Functions

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • Fatih Hezenci,
  • Hüseyin Budak,
  • Muhammad Amer Latif

摘要

We propose a new method for the investigation of integral identities according to tempered fractional operators. In addition, we prove the midpoint-type and trapezoid-type inequalities by using twice-differentiable convex functions associated with tempered fractional integral operators. We use the well-known Hölder inequality and the power-mean inequality in order to obtain inequalities of these types. The resulting Hermite–Hadamard-type inequalities are generalizations of some investigations in this field, involving Riemann–Liouville fractional integrals.