Integral inequalities for twice differentiable functions by novel fractional operator

Abstract

This paper presents new integral inequalities for twice differentiable (\Lambda,\delta)-convex functions involving extended weighted fractional integrals. By leveraging a fundamental identity and employing Hölder, Power mean and Young inequalities under various convexity conditions on the derivative, we generalize and refine Hermite-Hadamard type inequalities. Applications to Riemann-Liouville, Caputo-Fabrizio and Atangana-Baleanu fractional integral operators demonstrate the broad applicability of the results.