This reconstructed study develops an integrated mathematical and operational architecture in which distributional integral transforms provide the analytical layer for resilient smart logistics. The framework retains the original testing-function-space construction, its seminorm topology, Fréchet-space completeness, dual-space characterization, fractional reaction–diffusion formulation, Mittag-Leffler representation, and Talbot inversion. Around this mathematical core, the study adds a genuine logistics interpretation through two-sided FKF/FKL spectral analysis, sequential convergence, time-shift and exponential-modulation behavior, residue-based resonance extraction, and shift-invariant analysis of multi-echelon lead times. The resulting spectral state is connected to digital-twin telemetry, Internet of Things sensing, green logistics indicators, blockchain traceability with hash-chain provenance, Industry 5.0 humancentric automation, swipe authorization, anti-theft signaling, hybrid-electric mobility, and quantum-annealing QUBO models for constrained Unit Load Device dispatch. The objective is not to replace the underlying equations but to show how the same distributional machinery can support heterogeneous physical and cyber-physical supply-chain signals while preserving mathematical consistency.

A. Tale, V. A. Sharma,"Distributional FKF–FKL Spectral Framework for Resilient Smart Logistics with Digital Twins, Sustainable Mobility, and Quantum-Constrained Dispatch" International Journal of Advanced Multidisciplinary Research and Educational Development, V2(5): Page(337-341) September - October 2026. ISSN: 3107-6513. www.ijamred.com. Published by Scientific and Academic Research Publishing.