| Summary: | In this article, we look at a variety of mean-type integral inequalities for a well-known Hilfer fractional derivative. We consider twice differentiable convex and <i>s</i>-convex functions for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>s</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></semantics></math></inline-formula> that have applications in optimization theory. In order to infer more interesting mean inequalities, some identities are also established. The consequences for Caputo fractional derivative are presented as special cases to our general conclusions.
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