On the maximum principle for the multi-term fractional transport equation

TL;DR

This paper establishes maximum and comparison principles for multi-term space-time-fractional transport equations, ensuring uniqueness and stability of solutions, and extends these principles to unbounded domains for time-fractional transport equations.

Contribution

It introduces a maximum principle for multi-term space-time-fractional transport equations and applies it to prove solution uniqueness and comparison principles.

Findings

Maximum principle for multi-term fractional transport equations

Uniqueness of solutions to initial-boundary-value problems

Comparison principles for solutions with different data

Abstract

In this paper, we prove a maximum principle for the general multi-term space-time-fractional transport equation and apply it for establishing uniqueness of solution to an initial-boundary-value problem for this equation. We also derive some comparison principles for solutions to the initial-boundary-value problems with different problem data. Finally, we present a maximum principle for the Cauchy problem for a time-fractional transport equation on an unbounded domain.