  We employ Mittag-Leffler type kernels to solve a system of fractional
differential equations using fractal-fractional (FF) operators with two fractal
and fractional orders. Using the notion of FF-derivatives with nonsingular and
nonlocal fading memory, a model of three polluted lakes with one source of
pollution is investigated. The properties of a non-decreasing and compact
mapping are used in order to prove the existence of a solution for the FF-model
of polluted lake system. For this purpose, the Leray-Schauder theorem is used.
After exploring stability requirements in four versions, the proposed model of
polluted lakes system is then simulated using two new numerical techniques
based on Adams-Bashforth and Newton polynomials methods. The effect of
fractal-fractional differentiation is illustrated numerically. Moreover, the
effect of the FF-derivatives is shown under three specific input models of the
pollutant: linear, exponentially decaying, and periodic.
