# Mathematical Analysis of Conducting and Dielectric Sphere in Fractional Space

## Mathematical Analysis of Conducting and Dielectric Sphere in Fractional Space

## DOI:

https://doi.org/10.53560/PPASA(59-4)667## Keywords:

Laplacian Equation, Fractional Space, Dielectric Sphere, Separable Method## Abstract

This paper presents an analytical analysis of a sphere placed in fractional dimensional space. The Laplacian Equation in fractional space describes physics as a complex phenomenon. The general solution of the Laplacian equation in fractional space is obtained by the separable variable technique. We have investigated a close form solution for conducting sphere and dielectric sphere. Further, the electric potential and charge density, induced due to a point charge is calculated in fractional space, and also the energy radiated by the sphere is determined. The results are compared with the classical results by setting the fractional parameter α = 3 which normally lies in the limit 2 < α ≤ 3.

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## How to Cite

*Proceedings of the Pakistan Academy of Sciences: A. Physical and Computational Sciences*,

*59*(4), 61–65. https://doi.org/10.53560/PPASA(59-4)667