Synthesis of Generalized Laplace-Meijer (LK) Transforms and Meijer G-Functions: Extensions and Applications in Sustainable Transportation and Industrial Resilience

This paper explores combinations of the generalized Laplace-Meijer (LK) transform, originally developed in distributional settings, with contemporary engineering challenges. Building on the representation theorem for the LK transform (Gulhane & Gudadhe, 2006), we synthesize its kernel involving modified Bessel functions expressed via Meijer G-functions with applications in battery sizing for plug-in hybrid electric vehicles, advancements in automotive batteries, and resilience modeling in global supply chains. Novel combinations include using LK/Meijer G transforms for solving differential equations governing battery dynamics, energy management in hybrid architectures, and stochastic modeling of supply chain disruptions. Practical examples demonstrate improved analytical solutions for impulsive signals and system responses in EV contexts. Results highlight enhanced modeling accuracy and resilience strategies, contributing to sustainable transportation and industrial systems.