Linear barycentric rational collocation method for solving nonlinear time-fractional Cable equation

The time-fractional Cable (TFC) equation constitutes a significant advancement of the classical Cable equation within the context of fractional calculus. In contrast to conventional numerical techniques such as finite difference and finite element methods, the barycentric interpolation method exhibits superior capability in handling the nonlocal properties inherent in fractional operators. This study thoroughly examines the principles and attributes of the barycentric interpolation method, integrating them with the unique aspects of the TFC equation to develop an appropriate matrix formulation. This transformation facilitates the conversion of the TFC equation into a solvable algebraic system. The proposed algorithm's accuracy and convergence rate are meticulously evaluated. Numerical experiments are performed to underscore the benefits of this approach in solving the TFC equation, thereby confirming the efficacy of the error analysis and convergence assessment.