Abstract
In this paper, the study of linear differential equations involving one conventional and two nilpotent variables is started. This is a natural extension of the case of one involved nilpotent (para-Grassmann) variable studied earlier. In the case considered here, the two nilpotent variables are assumed to commute, hence they are generators of a (generalized) zeon algebra. Using the natural para-supercovariant derivatives $$D_i$$ transferred from the study of a para-Grassmann variable, we consider linear differential equations of order at most two in $$D_i$$ and discuss the structure of their solutions. For this, convenient graphical representations in terms of simple graphs are introduced.
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