Unifying Transforms for Singular Cauchy Problems in Quantum Logistics, Supply Chain Resilience, and Energy Systems

DOI

https://www.doi.org/10.59256/ijire.20260704010

Published In

Volume 7, Issue 4 (2026)

Published Online

July-August 2026

Pages

71-76

Article Type

Original Article

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This paper introduces a novel framework of creatively equipped convex topological spaces to address challenges in theoretical forward models. We extend the Gelfand–Shilov technique to generalize the Laplace–Stieltjes transform via a simple objective function that combines two transforms in the distributional sense. Appropriate domains support harmonic analysis under distributional conditions. The framework offers tools for modeling and analyzing Cauchy problems and PDEs with distributional data. The primitive operator provides clear explanations in general settings. Extending to higher dimensions yields faster decay rates, even in polynomial cases, relying on strong continuity at the origin implying continuity at every point. It accommodates solutions lacking continuity at zero, common in practical applications.