Unified Operator Transform Framework for Integral Representations

This research introduces a unified operator transform framework that generalizes classical integral transforms such as Laplace, Mellin, and Hankel. By embedding operator-based kernels and derivative mappings, the paper constructs a coherent model capable of linking classical and modern transform identities within a single analytical structure. The approach establishes a foundation for a broader operator-based analysis of special functions and non-elementary integrals.