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

Author

Listed:
  • Weerawat Sudsutad

    (Department of Statistics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, Thailand
    These authors contributed equally to this work.)

  • Nantapat Jarasthitikulchai

    (Department of General Education, Faculty of Science and Health Technology, Navamindradhiraj University, Bangkok 10300, Thailand
    These authors contributed equally to this work.)

  • Chatthai Thaiprayoon

    (Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, Thailand
    Center of Excellence in Mathematics, CHE, Sri Ayutthaya Rd., Bangkok 10400, Thailand
    These authors contributed equally to this work.)

  • Jutarat Kongson

    (Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, Thailand
    Center of Excellence in Mathematics, CHE, Sri Ayutthaya Rd., Bangkok 10400, Thailand
    These authors contributed equally to this work.)

  • Jehad Alzabut

    (Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
    Department of Industrial Engineering, OSTİM Technical University, Ankara 06374, Turkey
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Weerawat Sudsutad & Nantapat Jarasthitikulchai & Chatthai Thaiprayoon & Jutarat Kongson & Jehad Alzabut, 2022. "Novel Generalized Proportional Fractional Integral Inequalities on Probabilistic Random Variables and Their Applications," Mathematics, MDPI, vol. 10(4), pages 1-21, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:573-:d:747726
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    References listed on IDEAS

    as
    1. Jehad Alzabut & Weerawat Sudsutad & Zeynep Kayar & Hamid Baghani, 2019. "A New Gronwall–Bellman Inequality in Frame of Generalized Proportional Fractional Derivative," Mathematics, MDPI, vol. 7(8), pages 1-15, August.
    2. Weerawat Sudsutad & Sotiris K. Ntouyas & Jessada Tariboon, 2014. "Fractional Integral Inequalities via Hadamard’s Fractional Integral," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-11, April.
    3. repec:kap:iaecre:v:14:y:2008:i:4:p:433-440 is not listed on IDEAS
    4. Saima Rashid & Fahd Jarad & Yu-Ming Chu, 2020. "A Note on Reverse Minkowski Inequality via Generalized Proportional Fractional Integral Operator with respect to Another Function," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-12, April.
    5. Samih Azar, 2008. "Jensen’s Inequality in Finance," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 14(4), pages 433-440, November.
    6. Atangana, Abdon, 2017. "Fractal-fractional differentiation and integration: Connecting fractal calculus and fractional calculus to predict complex system," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 396-406.
    7. Sotiris K. Ntouyas & Sunil D. Purohit & Jessada Tariboon, 2014. "Certain Chebyshev Type Integral Inequalities Involving Hadamard’s Fractional Operators," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, May.
    8. Abdullah Akkurt & Zeynep Kaçar & Hüseyin Yildirim, 2015. "Generalized Fractional Integral Inequalities for Continuous Random Variables," Journal of Probability and Statistics, Hindawi, vol. 2015, pages 1-7, January.
    9. Jessada Tariboon & Sotiris K. Ntouyas & Weerawat Sudsutad, 2014. "Some New Riemann-Liouville Fractional Integral Inequalities," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2014, pages 1-6, March.
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