Weighted fractional inequalities for new conditions on h-convex functions

We use a new function class called B-function to establish a novel version of Hermite-Hadamard inequality for weighted psi-Hilfer operators. Additionally, we prove two new identities involving weighted psi-Hilfer operators for differentiable functions. Moreover, by employing these equalities and the properties of the B-function, we derive several trapezoid- and midpoint-type inequalities for h-convex functions. Furthermore, the obtained results are reduced to several well-known and some new inequalities by making specific choices of the function h.