Numerical solution for fractional differential equations by using Jacobi–Gauss–Radau collocation method

This study proposes a novel numerical approach for addressing both linear and nonlinear initial fractional order differential equations (FDEs) through the implementation of the Jacobi–Gauss–Radau (JGR) integrated with Caputo fractional derivatives. The problem is effectively transformed into a simplified system of FDEs, encompassing the unknown coefficients, by employing shifted JGR points for the FDEs and their initial conditions. For the purpose of investigating the effectiveness and accuracy of the introduced method, some numerical illustrations are provided for various linear and nonlinear FDEs.