Close Form Solution for Dielectric Cylindrical Shell in Fractional Dimensional Space

Close Form Solution for Dielectric Cylindrical Shell in Fractional Dimensional Space


  • Saeed Ahmed Department of Electronics, Quaid-i-Azam University, Islamabad, Pakistan.
  • Muhammad Akbar Department of Earth Sciences, Quaid-i-Azam University, Islamabad, Pakistan.
  • Muhammad Imran Shahzad Department of Applied Physics, Federal Urdu University of Arts, Science and Technology, Islamabad, Pakistan.



Fractional dimensional –Space, Laplacian-equation, Dielectric coated cylinder, Electric potential, Analytical Solution, Method of Separation Variables


We have studied the Laplacian equation in non-integer space which had been previously used to describe complex phenomena in physics and electromagnetism. We have applied this idea to a dielectric cylindrical shell to find the electric potential and field of a dielectric coated cylinder analytically in fractional dimensional space. The problem is derived using Gegenbauer polynomials. This close form gneral solution solved in fractional dimensional space can be applied for various materials of cylindrical shell, outside shell and inside the cylindrical core. The obtained solution is retrieved for integer order by setting the fractional parameter α=3.


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How to Cite

Ahmed, S. ., Akbar, M. ., & Imran Shahzad, M. . (2022). Close Form Solution for Dielectric Cylindrical Shell in Fractional Dimensional Space: Close Form Solution for Dielectric Cylindrical Shell in Fractional Dimensional Space. Proceedings of the Pakistan Academy of Sciences: A. Physical and Computational Sciences, 59(2), 43–46.