On generalizations of some integral inequalities via lidstone green functions

In this paper, we generalize the classical Hermite-Hadamard, Ostrowski, and Simpson type integral inequalities by using Lidstone interpolation polynomials and their associated Green functions. By incorporating the Riemann-Liouville fractional integral operator, we construct novel Ostrowski and Simpson-type inequalities whose remainder estimates are explicitly expressed in terms of fractional integrals and Lidstone-Green kernels. Our results contribute to the interplay between fractional calculus, interpolation theory, and classical analysis.