What question did this study set out to answer?

This research aims to enhance the original D(t) imbalance model to address chronic and cumulative diseases through historical data dependency.

May 1, 2026Open Access

9-Keel Unified Theory Series: Paper 45 Fractional-Order D(t) Model with Memory Kernel for Chronic & Cumulative Diseases

Puntos clave

This research aims to enhance the original D(t) imbalance model to address chronic and cumulative diseases through historical data dependency.
Extended the original D(t) model using a fractional-order derivative.
Incorporated a power-law memory kernel to account for historical dependency.
Maintained the overall 9-Keel framework while adapting to new disease classifications.
Proposed a new theoretical structure that is applicable to diseases requiring historical context.
Demonstrated potential for the model to explain disease progression over time.

Resumen

The original D(t) imbalance model (Papers 36–40) successfully unified acute critical illnesses (DKA, cytokine storm, MODS, etc.) using a first-order, memoryless differential equation. However, chronic, degenerative, and cumulative diseases (Alzheimer’s, COPD, Parkinson’s, silicosis) require historical dependency – damage built up over years. This paper extends D(t) with a fractional-order derivative and a power-law memory kernel, keeping the 9-Keel framework intact while covering a new class of diseases without rewriting the theory. This study is a pure theoretical analysis and does not involve clinical diagnosis, treatment, or medical guidance.

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