This study presents a local meshless method based on radial basis functions for the numerical solution of the nonlinear time-fractional Burgers’ equation (TFBE) involving the fractional derivatives of Caputo (CFD) and Caputo–Fabrizio (CFFD). Time is discretized using the implicit finite difference scheme with $\theta = 1$ , while radial basis functions (RBFs), which do not require a mesh to approximate the solution, are used for spatial discretization. The Rubin–Graves technique is used to linearize nonlinear terms. Approximation of the existing spatial derivatives is done using central and finite difference methods, and the temporal derivatives are approximated by using the definition of Caputo and Caputo–Fabrizio derivatives. With the mentioned techniques, a system of algebraic equations is established. By comparing the results obtained from solving this system with the previous results, it is clear that the presented technique provides accurate, stable, and convergent results.
