On the equivalence of viscosity solutions and distributional solutions for the time-fractional diffusion equation

TL;DR

This paper proves that viscosity solutions and distributional solutions are equivalent for the initial-boundary value problem of the time-fractional diffusion equation, clarifying the theoretical foundation of solution concepts in fractional diffusion models.

Contribution

It establishes the equivalence between viscosity and distributional solutions for the time-fractional diffusion equation, a key step in understanding solution behavior.

Findings

Proves the equivalence of solution notions for fractional diffusion.

Provides theoretical foundation for fractional PDE solutions.

Clarifies solution concepts in fractional diffusion models.

Abstract

We consider an initial-boundary value problem for the time-fractional diffusion equation. We prove the equivalence of two notions of weak solutions, viscosity solutions and distributional solutions.