Title: Z-Fractional Differential Equations in Medical Science

 

Abstract:

This talk introduces a unified framework of Z‑fractional differential equations for modeling medical systems where both uncertainty and long‑term memory are essential. Z‑numbers encode imprecise clinical information together with reliability, while generalized Hukuhara–Caputo fractional derivatives capture temporal memory and nonlocal biological effects. Two applications are presented. The first develops a Z‑fractional system for demyelination–remyelination dynamics in Multiple Sclerosis (MS), incorporating immune activity, inflammation, and blood–brain barrier gating. The second applies Z‑fractional diffusion to anti‑cancer drug release, where the diffusion coefficient, dose, and Hurst exponent are uncertain and represented as Z‑numbers. These examples demonstrate how uncertainty and memory can be addressed rigorously in biomedical modeling, motivating future work in numerical solvers, parameter identification, and Z‑based optimal control for personalized therapy.