Simpson-type inequalities for conformable fractional operators with respect to twice-differentiable functions

Authors

  • Fatih Hezenci Department of Mathematics, Faculty of Science and Arts, Duzce University, Turkiye
  • Huseyin Budak Department of Mathematics, Faculty of Science and Arts, Duzce University, Turkiye

Keywords:

Simpson-type inequality, fractional conformable integrals, fractional conformable derivatives, fractional calculus, convex function

Abstract

In this paper, we prove an equality for the case of twice-differentiable convex functions with respect to the conformable fractional integrals. With the help of this equality, we establish several Simpson-type inequalities for twice-differentiable convex functions by using conformable fractional integrals. Sundry significant inequalities are obtained by taking advantage of the convexity, the H\"{o}lder inequality, and the power mean inequality. By using the specific selection of our results, we give several new and well-known results in the literature.

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Published

2023-04-02

Issue

Vol. 17

Section

Vol. 17, No. 3, (2023)

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