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In this paper we present a novel way to mathematically frame the concept of ecological memory of plant water stress in the context of root water uptake in unsaturated flow equations. Inspired by recent eco-hydrological papers, we model the water absorption by roots with a non-local sink term, accounting also for a memory effect. In order to model such a memory effect, an integral equation is defined; the main purpose of this work is to provide sufficient conditions on the functions at play for ensuring existence and uniqueness of its solution. Finally, tailored numerical methods are implemented, and numerical simulations are also provided. • We mathematically frame the ecological memory of water stress by plant roots. • We model water absorption by roots by a non-local sink term. • We define an integral equation to model such a memory effect in Richards' equation. • We provide assumptions ensuring existence and uniqueness of its solution. • Tailored numerical methods are implemented, and numerical simulations are provided. [ABSTRACT FROM AUTHOR]