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International Journal of Creative and Open Research in Engineering and Management

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ISSN: 3108-1754 (Online)
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Volume 02, Issue 9

Published on: September 2026

HYBRID FKF–FKL TRANSFORM FRAMEWORK FOR DIGITAL-TWIN BATTERY SYSTEMS, SMART MOBILITY, AND RESILIENT QUANTUM LOGISTICS

Gupta AA

Shinde S

Department of Mathematics

Government College of Engineering, Amravati, Maharashtra, India
DOI:https://doi.org/10.55041/ijcope.v2i9.107

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Abstract

Battery systems, smart mobility, and resilient logistics generate observations that are temporal, scale-dependent, delayed, incomplete, and operationally constrained. This paper constructs a mathematical framework from the two-sided FKF transform, its time-shift property, and the testing-function-space and sequential-convergence foundations of the hybrid Fourier–Macdonald construction. The central construction uses a product kernel formed from a two-sided Fourier factor and an imaginary-order Macdonald factor. The Fourier coordinate represents temporal oscillation and delay, while the KL coordinate represents positive physical or operational scale. The resulting framework is extended to generalized observations so that impulses, switching events, abrupt demand shocks, and incomplete telemetry can be represented without forcing every event into a smooth classical signal. The theory is connected to automotive and electric-vehicle battery systems, smart mobility and intelligent transportation systems, spectral supply-chain analysis, quantum transportation and logistics, artificial intelligence and green supply chains, AI–blockchain traceability, digital twins, and resilience theory. Quantum annealing and QUBO formulation are placed after spectral validation, physical feasibility, and provenance checks. The proposed architecture therefore distinguishes prediction from authorization and treats quantum optimization as a downstream decision mechanism. Expanded operator relations are developed for delay, differentiation, residual spectra, resonance, energy feasibility, provenance, and binary logistics decisions. The framework provides a common mathematical language for battery telemetry, mobility states, multi-echelon delays, digital-twin residuals, and constrained quantum dispatch.

How to Cite this Paper

AA, G. (2026). Hybrid FKF–FKL Transform Framework for Digital-Twin Battery Systems, Smart Mobility, And Resilient Quantum Logistics. International Journal of Creative and Open Research in Engineering and Management, <i>02</i>(9), 1-9. https://doi.org/10.55041/ijcope.v2i9.107

AA, Gupta. "Hybrid FKF–FKL Transform Framework for Digital-Twin Battery Systems, Smart Mobility, And Resilient Quantum Logistics." International Journal of Creative and Open Research in Engineering and Management, vol. 02, no. 9, 2026, pp. 1-9. doi:https://doi.org/10.55041/ijcope.v2i9.107.

AA, Gupta. "Hybrid FKF–FKL Transform Framework for Digital-Twin Battery Systems, Smart Mobility, And Resilient Quantum Logistics." International Journal of Creative and Open Research in Engineering and Management 02, no. 9 (2026): 1-9. https://doi.org/https://doi.org/10.55041/ijcope.v2i9.107.

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  • •Published on: Sep 15 2026
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