Equations of motion in a non-integer-dimensional space

Gravitational potential in fractional space

“…In recent years, authors have redefined the integer space to the case of fractional space [3][4][5][6][7][8]. It is believed that the dimension of space plays an important role in quantum field theory, in the Ising limit of quantum field theory, in random walks and in Casimir effect [4].…”

General Solution for Waveguide Modes in Fractional Space

“…The abundance of fractals in nature resulted in research into the formulation of laws of physics for fractional spaces. Palmer and Stavrinou worked on equations of motion in a non-integer dimensional space [5]. Similarly, Tarasov analyzed Electromagnetic fields on fractals [6].…”

The Wave Equation and General Plane Wave Solutions in Fractional Space

“…Fractional-dimensional space concept is effectively used in many areas of physics to describe the physical description of confinement in low dimensional systems [1][2][3][4][5][6]. This approach is applied to replace the real confining structure with an effective space, where the measurement of its confinement is given by non-integer dimension [2,3].…”

“…This approach is applied to replace the real confining structure with an effective space, where the measurement of its confinement is given by non-integer dimension [2,3]. This confinement can be described in low dimensional system which can have different degree of confinement in different orthogonal directions, e.g., if we have system that is confined as 1.8 dimensional, then it could be described as 1 + 0.8 dimensional in two coordinates and as 1 + 0.2 + 0.6 dimensional in three coordinates, if dimensions add linearly [6]. Fractional calculus (a generalization of differentiation and integration to fractional order) is used by different authors to describe fractional solutions to many electromagnetic problems as well as fractional dimensional space [6-10, 16, 17].…”