In this study, we propose to derive an accurate numerical procedure to
solve the mathematical model which describes the electrical R-L circuit
composed of resistors and inductors driven by a voltage of current
source, which is the fractional-order model for the electrical
RL-circuit. Our study depends on the spectral collocation method via the
useful properties of the Chebyshev polynomials of the third-kind. Some
theorems about the convergence analysis are given. The study concludes
by comparing the resulting approximate solutions of the proposed model
with the exact solution in the classical case. Illustrative graphical
and numerical analysis of the derived results are also included in this
study.