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<p>In this study, we introduce new generalized multiplicative <i>h</i>-fractional integral and <i>h</i>-fractional derivative operators by employing multiplicative calculus within the framework of fractional analysis. Purely multiplicative operational arithmetic is utilized in deriving these results. The fundamental properties of the proposed operators are rigorously established. Furthermore, by means of the obtained generalized multiplicative <i>h</i>-fractional integral operators, a new Hermite-Hadamard inequality is derived. In addition, a trapezoidal-type inequality related to the Hermite-Hadamard inequality for the proposed generalized multiplicative <i>h</i>-fractional integrals is presented. The findings are further supported with illustrative examples and graphical representations.</p>

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Generalized multiplicative h-fractional integrals and derivatives with Hermite-Hadamard inequality

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月13日

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  • Umut Bas,
  • Huseyin Yildirim

摘要

In this study, we introduce new generalized multiplicative h-fractional integral and h-fractional derivative operators by employing multiplicative calculus within the framework of fractional analysis. Purely multiplicative operational arithmetic is utilized in deriving these results. The fundamental properties of the proposed operators are rigorously established. Furthermore, by means of the obtained generalized multiplicative h-fractional integral operators, a new Hermite-Hadamard inequality is derived. In addition, a trapezoidal-type inequality related to the Hermite-Hadamard inequality for the proposed generalized multiplicative h-fractional integrals is presented. The findings are further supported with illustrative examples and graphical representations.