Mathematical Analysis on Conducting Sphere Embedded in Non Integer Dimensional Space

Abstract

We have derived an analytical solution in low frequency using the idea of a fractional Laplacian equation. Fractional dimensional (FD) space has importance in describing the complex physics phenomena. Here, the Laplacian equation in spherical coordinated (r,θ,0) is expressed in fractional dimensional space using Gegenbauer polynomials. The analytical solution is obtained by the separation variable method. The general solution is a product of angular and radial solutions and is independent of ϕ due to azimuthal symmetry. The classical solution is retained by setting fractional parameter α=3. Further, numerical results are discussed for different values of α and compared with available literature.