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Fractional version of Hermite-Hadamard-Mercer inequalities for convex stochastic processes via Ψ<inf>k</inf> -Riemann-Liouville fractional integrals and its applications

Abstract:

In the present paper, authors derive some new Hermite-Hadamard-Mercer type inequalities for convex stochastic processes using Ψk -Riemann-Liouville fractional integrals. Furthermore, to civilized the paper we prove different lemmas to present unique refinements of Hermite-Hadamard-Mercer type inequalities. Also, we discuss some special cases of our proven results. These new inequalities yield several generalizations of previously known results. Finally, we develop some applications to special means.