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In this paper, certain Hermite–Hadamard–Mercer type inequalities are proved via k-Caputo fractional derivatives. We established some new k-Caputo fractional derivatives inequalities with Hermite–Hadamard–Mercer type inequalities for differentiable mapping $\psi^{(n)}$ whose derivatives in the absolute values are convex.

Some Hermite–Jensen–Mercer type inequalities for k-Caputo-fractional derivatives and related results