Analytical Solution for Cylindrical Shell of Permeable Material in Fractional Dimensional Space

Abstract

We have investigated the Laplacian equation in fractional dimensional space (FDS) that is widely used in physics to describe many complex phenomena. Using this concept, we have applied it on a cylindrical shell of permeable material to find the analytical solution of electric potential in FDS. The derivation of this problem is performed by applying Gegenbauer polynomials. The general solution has been obtained in a closed form in the FDS and can be applied to the cylindrical shell for different materials inside the cylinder core and outside the shell. By setting the fractional parameter α = 3, the derived solution is retrieved for the integer order.