Spectral Differential Properties of the Distributional FKF Transform with Applications to Resilient Supply-Chain Systems

Gulhane, Akarshan

doi:https://doi.org/10.55041/ijcope.v2i8.139

Volume 02, Issue 8

Published on: August 2026

SPECTRAL DIFFERENTIAL PROPERTIES OF THE DISTRIBUTIONAL FKF TRANSFORM WITH APPLICATIONS TO RESILIENT SUPPLY-CHAIN SYSTEMS

Akarshan Gulhane

PTC Software Inc.

DOI:https://doi.org/10.55041/ijcope.v2i8.139

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Abstract

This paper develops the distributional theory of the two-sided Fourier–Kontorovich–Lebedev (FKF) transform, a hybrid integral transform that combines the Fourier kernel in the temporal variable with the Macdonald (modified Bessel) kernel of imaginary order in a positive scale variable. The transform is extended to a broad class of generalized functions via a carefully constructed test-function space of Gelfand–Shilov type. Central attention is given to the spectral differential property associated with the modified-Bessel operator, which converts differential action in the positive variable into multiplication by −q² in the spectral domain. The property is expanded with higher-order operators, mixed Fourier–KL rules, and solution formulae for model linear PDEs. Applications of the FKF spectral differential property to supply-chain systems are developed in detail: multi-scale inventory dynamics, disruption-intensity resilience analysis, digital-twin spectral monitoring, and discrete numerical implementation for operational data. The framework is positioned within recent advances in intelligent logistics, digital twins, quantum-inspired optimization, and supply-chain resilience. Concrete recommendations for research and practice, together with a recommended computational form for discrete and noisy data, conclude the work.

How to Cite this Paper

Gulhane, A. (2026). Spectral Differential Properties of the Distributional FKF Transform with Applications to Resilient Supply-Chain Systems. International Journal of Creative and Open Research in Engineering and Management, <i>02</i>(8), 1-9. https://doi.org/10.55041/ijcope.v2i8.139

Gulhane, Akarshan. "Spectral Differential Properties of the Distributional FKF Transform with Applications to Resilient Supply-Chain Systems." International Journal of Creative and Open Research in Engineering and Management, vol. 02, no. 8, 2026, pp. 1-9. doi:https://doi.org/10.55041/ijcope.v2i8.139.

Gulhane, Akarshan. "Spectral Differential Properties of the Distributional FKF Transform with Applications to Resilient Supply-Chain Systems." International Journal of Creative and Open Research in Engineering and Management 02, no. 8 (2026): 1-9. https://doi.org/https://doi.org/10.55041/ijcope.v2i8.139.

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