<p>Conformable fractional integrals have gained increasing attention for their ability to generalize classical calculus while preserving key structural properties. Their adaptability has made them a valuable tool in the formulation and extension of analytical inequalities. Besides, the Newton inequality is particularly important due to its enhanced accuracy in approximation theory and its applications in numerical analysis. Motivated by the growing significance of these approaches, we focus on establishing weighted Newton-type inequalities for various classes of functions using conformable fractional integrals. A fundamental integral identity involving a positive weighted function is first derived, forming the analytical basis of our results. Using this identity within the conformable fractional framework, we obtain generalized forms of Newton-type inequalities that can be applied to a variety of function types, such as differentiable convex functions, bounded functions, Lipschitz functions, and functions of bounded variation. To improve understanding, we provide illustrative examples along with corresponding graphical interpretations. Our findings not only extend several known results in the literature but also highlight the potential of conformable fractional operators in addressing problems where classical fractional models may be limited or overly rigid.</p>

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Advances in Weighted Newton-Type Inequalities for Various Function Classes Through Conformable Fractional Integrals

  • İzzettin Demir,
  • Esra Üneş,
  • Fuat Usta

摘要

Conformable fractional integrals have gained increasing attention for their ability to generalize classical calculus while preserving key structural properties. Their adaptability has made them a valuable tool in the formulation and extension of analytical inequalities. Besides, the Newton inequality is particularly important due to its enhanced accuracy in approximation theory and its applications in numerical analysis. Motivated by the growing significance of these approaches, we focus on establishing weighted Newton-type inequalities for various classes of functions using conformable fractional integrals. A fundamental integral identity involving a positive weighted function is first derived, forming the analytical basis of our results. Using this identity within the conformable fractional framework, we obtain generalized forms of Newton-type inequalities that can be applied to a variety of function types, such as differentiable convex functions, bounded functions, Lipschitz functions, and functions of bounded variation. To improve understanding, we provide illustrative examples along with corresponding graphical interpretations. Our findings not only extend several known results in the literature but also highlight the potential of conformable fractional operators in addressing problems where classical fractional models may be limited or overly rigid.