Some new parameterized inequalities based on Riemann-Liouville fractional integrals

Kara H., Budak H., Akdemir A. O.

FILOMAT, no.23, pp.7867-7880, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Publication Date: 2023
  • Doi Number: 10.2298/fil2323867k
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED)
  • Page Numbers: pp.7867-7880
  • Kocaeli University Affiliated: No

Abstract

In this article, we first obtain an identity that we will use throughout the article. With the help of this equality, new inequalities involving a real parameter are established for Riemann-Liouville fractional integrals. For this purpose, properties of the differentiable convex function, Ho & BULL;lder inequality, and power -mean inequality are used. In addition, new results are established with special choices of parameters in all proven inequalities. Our results are supported by examples and graphs. It is shown that some of these results generalize the trapezoid type and Newton-type inequalities.