Pre-Grüss inequality involving conformable fractional integrals and its applications for random variables

Abstract

In this study, some pre-Grüss type results involving conformable fractional integrals are derived. Afterward, novel inequalities involving cumulative distribution function, conformable fractional expectation value and moment, and conformable variance of the random variable pdf of which is bounded are obtained. Lastly, by means of inequalities presented in this work, some estimates of composite quadrature rules are provided.

Subject Classification:

• (2010) 60E15
• 26D07
• 26D15
• 26A33

Keywords:

• Grüss inequality
• Conformable fractional integrals
• Random variables