From the solutions of diffusion equation to the solutions of subdiffusive one

TL;DR

This paper develops exact Green's function solutions for subdiffusive equations with mixed boundary conditions, enabling analysis of systems with different transport regimes, exemplified by a two-part system with normal diffusion and subdiffusion.

Contribution

It introduces a method to construct exact time-dependent Green's functions for subdiffusive equations with complex boundary conditions, applicable to multi-part systems with different transport types.

Findings

Derived explicit Green's functions for subdiffusive systems

Solved for a two-part system with normal diffusion and subdiffusion

Facilitated analysis of concentration profiles in mixed transport systems

Abstract

Starting with the Green's functions found for normal diffusion, we construct exact time-dependent Green's functions for subdiffusive equation (with fractional time derivatives), with the boundary conditions involving a linear combination of fluxes and concentrations. The method is particularly useful to calculate the concentration profiles in a multi-part system where different kind of transport occurs in each part of it. As an example, we find the solutions of subdiffusive equation for the system composed from two parts with normal diffusion and subdiffusion, respectively.