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<p>In this paper, we establish a novel Boole-type identity associated with conformable fractional integrals for twice-differentiable functions. By incorporating second-order derivatives, we derive sharper inequalities and obtain improved error estimates for numerical integration formulas. Furthermore, several new conformable fractional Boole-type inequalities are developed under the assumption that the absolute value of the second derivative is convex. Finally, we investigate applications of the obtained results to special means and the modified Bessel function. Explicit error bounds and numerical examples are provided to illustrate the accuracy and effectiveness of the proposed inequalities.</p>

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Refined fractional boole-type inequalities via conformable fractional integrals for twice-differentiable convex functions with applications

  • 期刊论文

  • 发表日期：

    2026年6月1日

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  • Murti Yashobant Kumar,
  • Madan Mohan Soren

摘要

In this paper, we establish a novel Boole-type identity associated with conformable fractional integrals for twice-differentiable functions. By incorporating second-order derivatives, we derive sharper inequalities and obtain improved error estimates for numerical integration formulas. Furthermore, several new conformable fractional Boole-type inequalities are developed under the assumption that the absolute value of the second derivative is convex. Finally, we investigate applications of the obtained results to special means and the modified Bessel function. Explicit error bounds and numerical examples are provided to illustrate the accuracy and effectiveness of the proposed inequalities.