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<p>In this paper, we investigate a novel approach to studying an integral identity involving generalized Riemann-Liouville fractional operators. By employing this identity, several Newton-type inequalities are established for differentiable <i>p</i>-convex functions. Furthermore, we explore some more refined results by using Hölder and power-mean inequalities. We also derive a Newton-type inequality associated with generalized Riemann-Liouville fractional integrals for functions for bounded variation. The validity and effectiveness of the obtained results are illustrated graphically. Finally, we discuss applications of the main inequalities to demonstrate their significance. The findings suggest that these newly derived inequalities extend and generalize existing results previously reported in the literature.</p>

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Fractional inequalities of Newton-type for differentiable functions with applications

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年5月11日

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  • Muhammad Samraiz,
  • Muhammad Abu Bakar Ashraf,
  • Saima Naheed

摘要

In this paper, we investigate a novel approach to studying an integral identity involving generalized Riemann-Liouville fractional operators. By employing this identity, several Newton-type inequalities are established for differentiable p-convex functions. Furthermore, we explore some more refined results by using Hölder and power-mean inequalities. We also derive a Newton-type inequality associated with generalized Riemann-Liouville fractional integrals for functions for bounded variation. The validity and effectiveness of the obtained results are illustrated graphically. Finally, we discuss applications of the main inequalities to demonstrate their significance. The findings suggest that these newly derived inequalities extend and generalize existing results previously reported in the literature.