University of Tabriz Computational Methods for Differential Equations 2345-3982 Articles in Press 2026 01 15 Implicit numerical approach for nonlinear fractional differential equations with a time non-sigular kernel and mixed boundary conditions 21143 10.22034/cmde.2025.62977.2807 EN Leyla Azami Department of Applied Mathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, Iran. Amir Hossein Refahi Sheikhani Department of Applied Mathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, Iran. Hashem Saberi Najafi Department of Applied Mathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, Iran. Journal Article 2024 08 22 This study focuses on the numerical solution of the time-fractional nonlinear Cable equation with the Caputo–Fabrizio derivative using an implicit Crank–Nicolson scheme. To demonstrate the versatility and robustness of the proposed method, we investigate the problem under both Dirichlet and Neumann boundary condition. The Stability analysis confirms that the scheme is unconditionally stable. To further evaluate the robustness of the difference scheme, the same numerical framework is applied to the fractional Burgers equation under identical settings. Numerical experiments are conducted to verify the stability and accuracy of the method, and to illustrate its applicability in simulating both signal propagation in nerve fibers (cable equation) and viscous transport (Burgers equation). https://cmde.tabrizu.ac.ir/article_21143_4a8c6766385e8f52d1953a12c491ab72.pdf