In this article, the so-called fractional nonlinear space-time wave-diffusion equation is presented and discussed. This equation is solved by the similarity method using fractional derivatives in the Caputo, Riesz-Feller, and Riesz senses. Some particular cases are presented and the corresponding solutions are shown by means of 2-D and 3-D plots.
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.
AMS Subject Classification: 30G99, 30E99Key Words: quaternions, Laplace's equations, quate
Initial ProvisionsThroughout this work, are considered quaternionic functions which follow the pattern f i (t, x, y, z), with i = 1, 2, 3, 4, where t is the time and the coordinates x, y and z are considered the spatial coordinates. Thus, the quaternion q is written here as follows;The next section based on a paper by Borges and Machado [2] shows a set
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 [1]. 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.
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