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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
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.