Line integration and second order partial differential equations over Cayley-Dickson algebras

TL;DR

This paper explores line integration of generalized functions and investigates second order partial differential equations with variable coefficients over Cayley-Dickson algebras, introducing formulas and solutions using non-commutative integration.

Contribution

It introduces a non-commutative line integration method for solving PDEs over Cayley-Dickson algebras with variable coefficients, expanding the analytical tools available.

Findings

Formulas for integrating PDEs over Cayley-Dickson algebras are derived.

Solutions to specific PDE examples are provided.

The approach handles piecewise continuous and generalized variable coefficients.

Abstract

Line integration of generalized functions is studied. Second order partial differential equations with piecewise continuous and generalized variable coefficients over Cayley-Dickson algebras are investigated. Formulas for integrations of such equations are deduced. For this purpose a non-commutative line integration is used. Examples of solutions of partial differential equations are given.