This paper introduces the LW transform, which fuses the classical Laplace transform with Weierstrass Gaussian smoothing to embed built-in regularization for dynamic systems. We present a corrected existence theorem, an explicit inversion formula, a convolution theorem, fractional-order operational calculus, and stable numerical methods. These advances enable efficient, robust solutions to linear and integro-differential equations even with noisy or incomplete data.

The framework is applied to electric vehicle battery systems for lithium-ion modeling, parameter estimation, SoC/SoH analysis, and hybrid optimization under thermal constraints. It is further applied to resilient supply chains to model inventory dynamics with lead time delays, disruption recovery, and bullwhip-effect mitigation. The approach yields computationally tractable tools for system modeling and digital twins. Future work focuses on hybrid quantum classical methods that leverage quantum annealing for largescale logistics optimization.