Work

Well-Posedness of Flux–Fractional Compartment Models and Their State Sensitivity Systems

Year: 2026

Type: article

Abstract: We studied flux–fractional compartment models with Caputo memory terms and their associated state sensitivity systems. The state, classical parameter sensitivities, and fractional-order sensitivity are formulated within a unified linear Volterra framework. Using a Sobolev-space formulation and an equivalent Bielecki norm, we establish existence and uniqueness in W1,p(0,T;H) on arbitrary finite time intervals. We further prove continuous differentiability of the parameter-to-solution map and derive a dimensionally consistent fractional-order sensitivity involving a dimensionless logarithmic kernel. The theory is illustrated by a one-compartment model with explicit Mittag–Leffler representations and relative sensitivity analysis.

Source: Mathematics

DOI: 10.3390/math14183301

Author: Mostafa Bachar

Institution: King Saud University

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: King Saud University