Year: 2026
Type: article
Abstract: This paper introduces and develops the two-sided Fourier–Kontorovich–Lebedev (FKF) transform, a hybrid integral transform that combines the classical Fourier kernel with the Macdonald function (modified Bessel function of the second kind) of imaginary order. The FKF transform is specifically adapted to signals defined on the half-plane of time and a positive scale variable, making it particularly suitable for the spectral analysis of supply-chain processes. We establish the fundamental definition, the underlying differential structure induced by the Macdonald equation, and key operational properties, with a detailed treatment and rigorous proofs of the multiplication-by-time and differentiation theorems in the Fourier domain. Applications are presented to demand intensity analysis, continuous inventory balance equations, the spectral characterization of the bullwhip effect, transportation lead-time phase shifts, and the quantitative assessment of disruption signatures. The resulting spectral framework provides frequency and scale resolved diagnostics that complement contemporary approaches based on digital twins, artificial intelligence, blockchain-enabled transparency, and Industry 5.0 human-centric automation. Limitations concerning numerical evaluation of the Macdonald function, inversion stability, and the transition from continuous to discrete supply-chain models are discussed. The work positions the FKF transform as a novel analytical instrument for resilience engineering and spectral control of modern logistics systems.
Author: A. Gulhane
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7203606182