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In the article, we establish serval novel Hermite–Jensen–Mercer-type inequalities for convex functions in the framework of the k -fractional conformable integrals by use of our new approaches. Our obtained results are the generalizations, improvements, and extensions of some previously known results, and our ideas and methods may lead to a lot of follow-up research.

New Hermite–Jensen–Mercer-type inequalities via k-fractional integrals