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This paper aims to establish generalized fractional integral inequalities for operators containing Mittag–Leffler functions. By applying <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>α</mi><mo>,</mo><mi>h</mi><mo>−</mo><mi>m</mi><mo>)</mo><mo>−</mo><mi>p</mi></mrow></semantics></math></inline-formula>-convexity of real valued functions, generalizations of many well-known inequalities are obtained. Hadamard-type inequalities for various classes of functions are given in particular cases.