A computational procedure and analysis for multi-term time-fractional Burgers-type equation

This paper presents a new numerical algorithm dealing with multi-term time-fractional Burgers-type equation involving the Caputo derivative. The proposed method consists of temporal discretization of L2$$ L2 $$ formula and spatial discretization using the exponential B-splines. The semi implicit approach is applied to discretize the nonlinear term u partial differential xu$$ u{\partial}_{\mathtt{x}}u $$. We adopt the Von-Neumann method to study stability. We also establish the convergence analysis. The proposed method is employed to solve a few numerical examples in order to test its efficiency and accuracy. Comparisons with the recent works confirm the efficiency and robustness of the proposed method.