Geometrical coupling fields of a hypercomplex type

This paper presents an application of Laplace's equation obtained from a quaternionic function that satisfies the Cauchy-Riemann conditions determined earlier by Borges and Machado [#!BorgesZeMarcio!#]. Therefore, we show that it is possible to express in a single equation gravity, electric and magnetic potential fields, and this expression can only be provided due to a function that will be called here the coupling function.

Geometrical hypercomplex coupling between electric and gravitational fields

The present work shows a coupling of electrical and gravitational fields through Cauchy-Riemann conditions for quaternions present in a previous paper [1]. It is also obtained an extended version of the Laplace-like equations for quaternions, now written in terms of both electric and gravitational fields.

Funções, funcionais e operadores na física matemática, com índices matriciais

With the advance of mathematical methods throughout the centuries, in particular with respect to the differential calculus, the notion of fractional derivative emerged with Leibniz and later developed by several well known scientists. Today that formalism is well used in the study of diffusion phenomena among other areas. We extend the fractional indices to matricial indices and develop a formalism to handle this generalized derivative, as well as other operators, functions and functionals in mathematical physics, originally defined for natural indices. Here we only consider 2x2 hermitian and anti-hermitian matrices. These matrices are associated to the well known Pauli matrices and Hamilton's quaternions. Applications with mathematical physics functions are presented