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The analysis of a dynamical system modelled by differential (continuum case)or difference equation (discrete case) with deformed exponential decay, here weconsider Tsallis and Kaniadakis exponentials, may require the use of therecently proposed deformed Lambert functions: the Lambert-Tsallis andLambert-Kaniadakis functions. In this direction, the present work studies thelogistic map with deformed exponential decay, using the Lambert-Tsallis and theLambert-Kaniadakis functions to determine the stable behaviour and the dynamicof the disentropy in the weak chaotic regime. Furthermore, we investigate themotion of projectile when the vertical motion is governed by a non-lineardifferential equation with Tsallis exponential in the coefficient of the secondorder derivative. In this case, we calculated the range of the projectile usingthe Lambert-Tsallis function.

Applications of Lambert-Tsallis and Lambert-Kaniadakis Functions in Differential and Difference Equations with Deformed Exponential Decay