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February 9, 2026Filomat1 citationsOpen Access

New (α,β)-order pre-Grüss fractional integral inequalities and applications for CRV

ZDZoubir DahmaniMSMehmet Sarikaya

Key Points

  • The research aims to derive new integral inequalities utilizing Riemann-Liouville fractional integrals, specifically focusing on the pre-Grüss inequalities.
  • Deriving two primary integral inequalities: ?-pre-Grüss inequality and (?, ?)-pre-Grüss inequality.
  • Employing Riemann-Liouville fractional integrals in the derivation process.
  • Discussing applications to continuous random variables with bounded probability density functions.
  • New estimates for integral inequalities are provided, extending existing literature.
  • Classical results are shown as special cases derived from the new findings.

Abstract

In this paper, we employ Riemann-Liouville fractional integrals to derive two primary integral findings concerning the ?-pre-Gr?ss inequality and the (?, ?)-pre-Gr?ss inequality. Our results extend existing integral inequalities reported in the literature. Additionally, we discuss some applications of our results for continuous random variables (CRV, for short) with bounded probability density functions. Some new estimates are provided in this context, along with classical results obtained as special cases from our results.

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Cite This Study

Dahmani et al. (2025) studied this question.

synapsesocial.com/papers/698979d9f0ec2af6756e7d1chttps://doi.org/10.2298/fil2510315d
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