| Summary: | This note generalizes several existing results related to Hermite–Hadamard inequality using <i>h</i>-Godunova–Levin and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi>h</mi><mn>1</mn></msub><mo>,</mo><msub><mi>h</mi><mn>2</mn></msub><mo>)</mo></mrow></semantics></math></inline-formula>-convex functions using a fractional integral operator associated with the Caputo–Fabrizio fractional derivative. This study uses a non-singular kernel and constructs some new theorems associated with fractional order integrals. Furthermore, we demonstrate that the obtained results are a generalization of the existing ones. To demonstrate the correctness of these results, we developed a few interesting non-trivial examples. Finally, we discuss some applications of our findings associated with special means.
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