Close Form Solution for Dielectric Cylindrical Shell in Fractional Dimensional Space

Abstract

We have studied the Laplacian equation in non-integer space which had been previously used to describe complex phenomena in physics and electromagnetism. We have applied this idea to a dielectric cylindrical shell to find the electric potential and field of a dielectric coated cylinder analytically in fractional dimensional space. The problem is derived using Gegenbauer polynomials. This close form gneral solution solved in fractional dimensional space can be applied for various materials of cylindrical shell, outside shell and inside the cylindrical core. The obtained solution is retrieved for integer order by setting the fractional parameter α=3.