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)

Muhammad Akbar Department of Physics, Air University,Islamabad,Pakistan

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

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

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

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.

Publication Details

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

References

References are not available for this document.

Citations

Citations are not available for this document.