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.
- Cauchy problem
- Comparison principle
- Initial-boundary-value problem
- Maximum principle
- Space-time-fractional multi-term transport equation
- Time-fractional transport equation