HERMITE HADAMARD TYPE INEQUALITIES FOR 𝜓-RIEMANN LIOUVILLE FRACTIONAL CONFORMABLE INTEGRALS VIA CONVEX FUNCTIONS

In this paper, we introduce a novel integral operator, termed as ψ-Riemann-Liouville fractional conformable integral operator, which extends the concept of fractional conformable integration. We also present a result concerning the Hermite-Hadamard dual inequality for the class of convex functions, incorporating this newly introduced operator. Additionally, we establish an identity for differentiable functions within the scope of the aforementioned operator. Furthermore, using this identity and employing various techniques, we derive several results associated with Hermite-Hadamard type inequalities for convex functions incorporating ψ-Riemann-Liouville fractional conformable integral operator. These findings extend and build upon prior research in the field.