Some new parameterized inequalities based on Riemann-Liouville fractional integrals

Abstract

In this article, we first obtain an identity that we will use throughout thearticle. With the help of this equality, new inequalities involving a realparameter are established for Riemann--Liouville fractional integrals. Forthis purpose, properties of the differentiable convex function, H\"{o}lderinequality, and power-mean inequality are used. In addition, new results areestablished with special choices of parameters in all proven inequalities.Our results are supported by examples and graphs. It is shown that some ofthese results generalize the trapezoid type and Newton-type inequalities.