A Derivation of GravitoElectroMagneticProca-type Equations in Fractional Space

Abstract

In a recent paper, M. Zubair et al. described a novel approach for fractional space generalization of the differential electromagnetic equations. A new form of vector differential operator Del and its related differential operators are formulated in fractional space. Using these modified vector differential operators, the classical Maxwell equations have been worked out for fractal media. In the meantime, there are other papers discussing fractional Maxwell equations. However, so far there is no derivation of Proca equations and GravitoElectroMagnetic Proca-type equations in fractional space. In this paper, I present for the first time a derivation of GravitoElectroMagnetic (GEM) Proca-type equations in fractional space. Considering that Proca equations may be used to explain some electromagnetic effect in superconductor, I suggest that fractional GEM Proca-type equations may be used to explain some gravitomagnetic effects of superconductor for fractal media. It is hoped that this paper may stimulate further investigations and experiments on gravitomagnetic effects.