| Summary: | Several fractional integral inequalities of the Hermite–Hadamard type are presented for the class of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>h</mi><mo>,</mo><mi>g</mi><mo>;</mo><mi>m</mi><mo>)</mo></mrow></semantics></math></inline-formula>-convex functions. Applied fractional integral operators contain extended generalized Mittag-Leffler functions as their kernel, thus enabling new fractional integral inequalities that extend and generalize the known results. As an application, the upper bounds of fractional integral operators for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>h</mi><mo>,</mo><mi>g</mi><mo>;</mo><mi>m</mi><mo>)</mo></mrow></semantics></math></inline-formula>-convex functions are given.
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