On Linear Differential Equations Involving a Para-Grassmann Variable

TL;DR

This paper explores linear differential equations with para-Grassmann variables, providing explicit solutions for low-order cases, establishing links to generalized Fibonacci numbers, and discussing various classes of such equations compared to classical ones.

Contribution

It introduces a foundational theory for differential equations involving para-Grassmann variables, including explicit solutions and connections to generalized Fibonacci numbers.

Findings

Explicit solutions for low-order equations provided

Connection established between para-Grassmann equations and generalized Fibonacci numbers

Discussion of various classes of differential equations involving para-Grassmann variables

Abstract

As a first step towards a theory of differential equations involving para-Grassmann variables the linear equations with constant coefficients are discussed and solutions for equations of low order are given explicitly. A connection to n-generalized Fibonacci numbers is established. Several other classes of differential equations (systems of first order, equations with variable coefficients, nonlinear equations) are also considered and the analogies or differences to the usual (''bosonic'') differential equations discussed.