AIMS Mathematics (Jan 2024)

A comprehensive review of Grüss-type fractional integral inequality

  • Muhammad Tariq,
  • Sotiris K. Ntouyas,
  • Hijaz Ahmad ,
  • Asif Ali Shaikh,
  • Bandar Almohsen ,
  • Evren Hincal

DOI
https://doi.org/10.3934/math.2024112
Journal volume & issue
Vol. 9, no. 1
pp. 2244 – 2281

Abstract

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A survey of results on Grüss-type inequalities associated with a variety of fractional integral and differential operators is presented. The fractional differential operators includes, Riemann-Liouville fractional integral operators, Riemann-Liouville fractional integrals of a function with respect to another function, Katugampola fractional integral operators, Hadamard's fractional integral operators, $ k $-fractional integral operators, Raina's fractional integral operators, tempered fractional integral operators, conformable fractional integrals operators, proportional fractional integrals operators, generalized Riemann-Liouville fractional integral operators, Caputo-Fabrizio fractional integrals operators, Saigo fractional integral operators, quantum integral operators, and Hilfer fractional differential operators.

Keywords