A Scale Frequency Spectral Framework Based on the FKF Transform for Resilient Supply Chains

A, Sharma V; M, Shinde S; G, Aayushee

doi:https://doi.org/10.55041/ijcope.v2i8.260

Volume 02, Issue 8

Published on: August 2026

A SCALE FREQUENCY SPECTRAL FRAMEWORK BASED ON THE FKF TRANSFORM FOR RESILIENT SUPPLY CHAINS

Sharma V A Shinde S M Aayushee G

Department of Mathematics, Smt. Narsamma Arts, Commerce and Science college, Amravati 444606

DOI:https://doi.org/10.55041/ijcope.v2i8.260

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Abstract

Modern supply chains operate as distributed, partially observed stochastic systems in which demand, lead times, quality, custody, energy state, and disruption information are revealed with delay and may be distorted across organizational boundaries. The supplied mathematical manuscript develops a distributional-transform perspective around Laplace and K-type kernels, modified Bessel functions, Meijer G-function representations, and second-order differential operators. This reconstruction extends that foundation toward intelligent and resilient supply-chain analysis by integrating the FKF spectral viewpoint with artificial intelligence, digital twins, trusted data exchange, Internet of Things sensing, sustainable mobility, and quantum-enabled logistics optimization. The FKF representation separates temporal oscillation from scale- or intensity-dependent behavior and provides a basis for studying multi-echelon lead-time dynamics, delayed information, resonance, and nonstationary disturbances. Distributional extension is particularly useful when operational signals are irregular, impulsive, incomplete, or generated by heterogeneous sensing systems. Artificial-intelligence models can consume spectral features for prediction and anomaly detection, while digital twins provide continuously updated operational context. Blockchain-oriented trusted records can preserve provenance and state consistency, and quantum optimization can address selected combinatorial logistics decisions.

Keywords— Sustainable Logistics; Green Supply Chain Management; Artificial Intelligence; Smart Transportation; Digital Twins; Blockchain; swipe controller; Energy-Efficient Logistics; Quantum Computing; Supply Chain Resilience; FKF Analysis.

How to Cite this Paper

A, S. V., M, S. S. & G, A. (2026). A Scale Frequency Spectral Framework Based on the FKF Transform for Resilient Supply Chains. International Journal of Creative and Open Research in Engineering and Management, <i>02</i>(8), 1-9. https://doi.org/10.55041/ijcope.v2i8.260

A, Sharma, et al.. "A Scale Frequency Spectral Framework Based on the FKF Transform for Resilient Supply Chains." 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.v2i8.260.

A, Sharma,Shinde M, and Aayushee G. "A Scale Frequency Spectral Framework Based on the FKF Transform for Resilient Supply Chains." 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.v2i8.260.

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