Analytical Solution for Cylindrical Shell of Permeable Material in Fractional Dimensional Space | [Proceedings of the Pakistan Academy of Sciences: A. Physical and Computational Sciences • 2023]

Author(s):

1. Muhammad Akbar: Department of Physics, Air University,Islamabad,Pakistan

2. Saeed Ahmed: Department of Physics, Quaid-i-Azam University,Islamabad,Pakistan

3. Muhammad Imran Shahzad: Department of Applied Physics, Federal Urdu University of Arts, Science and Technology,Islamabad,Pakistan

4. Muhammad Ahmad Raza: Department of Statistics, Federal Urdu University of Arts, Science and Technology,Islamabad,Pakistan

5. Sania Shaheen: Department of Applied Physics, Federal Urdu University of Arts, Science and Technology,Islamabad,Pakistan

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 diferent materials inside the cylinder core and outside the shell. By setting the fractional parameter a = 3, the derived solution is retrieved for the integer order.

Page(s): 69-72

DOI: 10.53560/PPASA(60-4)669

Published: Journal: Proceedings of the Pakistan Academy of Sciences: A. Physical and Computational Sciences, Volume: 60, Issue: 4, Year: 2023

Keywords:

General Close Form Solution , Gegenbauer Polynomials , Laplace Equation , Method of Separation Variable

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