Some New Refinements of Hermite–Hadamard-Type Inequalities Involving<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mrow><mml:mi>ψ</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>-Riemann–Liouville Fractional Integrals and Applications
Muhammad Uzair Awan, Sadia Talib, Yu‐Ming Chu, Muhammad Aslam Noor, Khalida Inayat Noor
Abstract
The main objective of this article is to establish some new fractional refinements of Hermite–Hadamard-type inequalities essentially using new<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:msub><mml:mrow><mml:mi>ψ</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>-Riemann–Liouville fractional integrals, where<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>k</mml:mi><mml:mo>></mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math>. Using this new fractional integral, we also derive two new fractional integral identities. Applications of the obtained results are also discussed.