NEW ψ - & (k, r)- FRACTIONAL CONFORMABLE INTEGRALS AND INEQUALITIES OF THE HERMITE–HADAMARD TYPE FOR POSITIVE–CONVEX STOCHASTIC PROCESSES

Abstract

Huang et al in the paper [Some inequalities of the Hermite–Hadamard Type for k-fractional conformable integrals, The Australian Journal of Mathematical Analysis and Applications, 16 (2019), no. 7, pp. 1-9] proved some new Hermite–Hadamard type inequalities for k-fractional conformable integrals for convex functions. In this paper, we extend and generalize the main result of the above-mentioned paper for (k, r)-fractional conformable integrals for positive–convex stochastic process and also point out a mistake (omission) in ([6], Theorem 3.1). In addition, we prove a new Hermite–Hadamard type inequality for ψ-fractional conformable integrals for positive–convex stochastic process.