Novel Generalized Proportional Fractional Integral Inequalities on Probabilistic Random Variables and Their Applications

Weerawat Sudsutad, Nantapat Jarasthitikulchai, Chatthai Thaiprayoon, Jutarat Kongson and Jehad Alzabut
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Weerawat Sudsutad: Department of Statistics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, Thailand
Nantapat Jarasthitikulchai: Department of General Education, Faculty of Science and Health Technology, Navamindradhiraj University, Bangkok 10300, Thailand
Chatthai Thaiprayoon: Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, Thailand
Jutarat Kongson: Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, Thailand
Jehad Alzabut: Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia

Mathematics, 2022, vol. 10, issue 4, 1-21

Abstract: This study investigates a variety of novel estimations involving the expectation, variance, and moment functions of continuous random variables by applying a generalized proportional fractional integral operator. Additionally, a continuous random variable with a probability density function is presented in context of the proportional Riemann–Liouville fractional integral operator. We establish some interesting results of the proportional fractional expectation, variance, and moment functions. In addition, constructive examples are provided to support our conclusions. Meanwhile, we discuss a few specific examples that may be extrapolated from our primary results.

Keywords: fractional expectation; fractional variance; fractional moment; proportional fractional integral operator; integral inequality; random variable (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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