Abstract :

The FKF Transform Is Introduced As A Two-variable Integral Transform That Combines The Fourier Kernel In A Temporal Or Longitudinal Variable With The Kontorovich–Lebedev Kernel Involving The Macdonald Function 𝐾𝑖𝑞(𝑥)in A Positive Spatial, Scale, Or Intensity Variable. Formulated Within A Distributional Framework On A Suitable Testing-function Space Over The Half-plane Ω = {(𝑡 , 𝑥) , : −∞ < 𝑡 < ∞ 𝑥 > 0}, The Transform Admits A Rigorous Analytic Continuation In The Fourier Spectral Variable And Supports Operator Identities That Convert Differential Structure In Both Variables Into Algebraic Factors In The Dual Variables (𝑠 , 𝑞). Fundamental Properties Are Established, Including Linearity, Time-shift And Modulation Theorems, Differentiation And Multiplication Rules, The Spectral Representation Of The Modified Bessel Operator, Analyticity On Strips In The Complex Plane, And Distributional Extension. These Properties Are Then Mapped Onto Supply-chain Signals That Jointly Depend On Time And A Nonnegative State Variable (inventory Level, Capacity Intensity, Disruption Magnitude, Transportation Distance, Etc.). Spectral Signatures In The (𝑠 , 𝑞)-domain Are Shown To Characterize Periodicity, Lead-time Delays, Scale-dependent Risk, Multi-echelon Propagation, And Transient Regime Changes. Conceptual Applications Are Developed For Inventory-risk Analysis, Productioncapacity Dynamics, Multi-echelon Networks, Monte-Carlo Spectral Uncertainty Quantification, And Real-time Digital-twin Monitoring. The Resulting Framework Supplies A Mathematically Coherent Bridge Between Classical Integral-transform Methods And Contemporary Data-rich, Multi Scale Supply Chain Problems, While Remaining Fully Compatible With Digital-twin Architectures, Resilience Analysis, And Hybrid AI Quantum Decision Systems

Published:

11-12-2025

Issue:

Vol. 25 No. 12 (2025)

Page Nos:

596-605

Section:

Articles

License:

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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