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

Sudsutad, Weerawat; Jarasthitikulchai, Nantapat; Thaiprayoon, Chatthai; Kongson, Jutarat; Alzabut, Jehad

doi:10.3390/math10040573

Open AccessArticle

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

by

Weerawat Sudsutad

^1,†

,

Nantapat Jarasthitikulchai

^2,*,†

,

Chatthai Thaiprayoon

^3,4,†

,

Jutarat Kongson

^3,4,*,†

and

Jehad Alzabut

^5,6,†

¹

Department of Statistics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, Thailand

²

Department of General Education, Faculty of Science and Health Technology, Navamindradhiraj University, Bangkok 10300, Thailand

³

Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, Thailand

⁴

Center of Excellence in Mathematics, CHE, Sri Ayutthaya Rd., Bangkok 10400, Thailand

⁵

Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia

⁶

Department of Industrial Engineering, OSTİM Technical University, Ankara 06374, Turkey

^*

Authors to whom correspondence should be addressed.

^†

These authors contributed equally to this work.

Mathematics 2022, 10(4), 573; https://doi.org/10.3390/math10040573

Submission received: 29 November 2021 / Revised: 27 January 2022 / Accepted: 10 February 2022 / Published: 12 February 2022

(This article belongs to the Special Issue Mathematical Inequalities with Applications)

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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

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MDPI and ACS Style

Sudsutad, W.; Jarasthitikulchai, N.; Thaiprayoon, C.; Kongson, J.; Alzabut, J. Novel Generalized Proportional Fractional Integral Inequalities on Probabilistic Random Variables and Their Applications. Mathematics 2022, 10, 573. https://doi.org/10.3390/math10040573

AMA Style

Sudsutad W, Jarasthitikulchai N, Thaiprayoon C, Kongson J, Alzabut J. Novel Generalized Proportional Fractional Integral Inequalities on Probabilistic Random Variables and Their Applications. Mathematics. 2022; 10(4):573. https://doi.org/10.3390/math10040573

Chicago/Turabian Style

Sudsutad, Weerawat, Nantapat Jarasthitikulchai, Chatthai Thaiprayoon, Jutarat Kongson, and Jehad Alzabut. 2022. "Novel Generalized Proportional Fractional Integral Inequalities on Probabilistic Random Variables and Their Applications" Mathematics 10, no. 4: 573. https://doi.org/10.3390/math10040573

APA Style

Sudsutad, W., Jarasthitikulchai, N., Thaiprayoon, C., Kongson, J., & Alzabut, J. (2022). Novel Generalized Proportional Fractional Integral Inequalities on Probabilistic Random Variables and Their Applications. Mathematics, 10(4), 573. https://doi.org/10.3390/math10040573

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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

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