New stochastic fractional integral and related inequalities of Jensen–Mercer and Hermite–Hadamard–Mercer type for convex stochastic processes

Abstract In this investigation, we unfold the Jensen–Mercer ( $\mathtt{J-M}$ J − M ) inequality for convex stochastic processes via a new fractional integral operator. The incorporation of processes, and operator having an exponential kernel brings direction to theory inequalities. With in mind, estimations Hermite–Hadamard–Mercer $\mathtt{H-H-M}$ H )-type inequalities involving are presented. context operator, also investigate novel identity differentiable mappings. Then, related -type is presented using as auxiliary result. Applications special means matrices These findings particularly appealing from perspective optimization, they provide larger analyze optimization mathematical programming problems.