Numerical approach for the fractional order cable model with theoretical analyses - Ali, Umair; Naeem, Muhammad; Ganie, Abdul Hamid; Fathima, Dowlath; Salama, Fouad Mohammad; Abdullah, Farah Aini (Frontiers in Physics, 2023)
In this study, the fractional order cable equation (FCE) in the sense of Riemann–Liouville fractional derivatives (R-LFD) is considered. We use a modified implicit finite difference approximation to solve the FCE numerically. The Fourier series approach is used to examine the proposed scheme's theoretical analysis, including stability and convergence. The scheme is shown to be unconditionally stable, and the approximate solution converges to the exact solution. To demonstrate the application and feasibility of the proposed approach, a numerical example is provided.