Mathematical Analysis on Conducting Sphere Embedded in Non Integer Dimensional Space

M Imran Shahzad; M Akbar; Saeed Ahmed

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Mathematical Analysis on Conducting Sphere Embedded in Non Integer Dimensional Space

Author(s)

M Imran Shahzad Department of Applied Physics, Federal Urdu University of Arts, Science and Technology, Islamabad, Pakistan

M Akbar Department of Electronics, Quaid-i-Azam University, Islamabad, Pakistan

Saeed Ahmed Department of Earth Sciences, Quaid-i-Azam University, Islamabad, Pakistan

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,0,0) 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 0 due to azimuthal symmetry. The classical solution is retained by setting fractional parameter a=3. Further, numerical results are discussed for different values of a and compared with available lterature.

Publication Details

Page(s) 83-87

DOI DOI not available

Published Journal: Proceedings of the Pakistan Academy of Sciences: A. Physical and Computational Sciences, Volume: 59, Issue: 1, Year: 2022

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Keywords

Fractional Dimensional Space, Separation Variable Method, Laplacian Equation, Analytical Solution

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