Numerical approximations for space-time fractional Burgers' equations via a new semi-analytical method

The objectives of this research describes a novel meshless technique for solving space-time fractional Burgers' equation by using concept of weighted and Caputo fractional derivative type. An efficient and accurate meshfree method based on backward substitution method and finite difference method is applied for problem on the various computational domain with scattering nodes. According to proposal method, Crank-Nicolson techniques is exploited to find the approximation in time level and the backward substitution method is utilized to compute node on the boundary. Subsequently, we obtain the corresponding weighted parameters the governing equations, we implemented collocation approach based on radial basis function. To eliminate nonlinearity, quasilinearization technique is applied to transform nonlinear source term into a linear source term. For investigation accuracy and reliably, this paper is compared with other previous researches. It is found that proposed scheme outperforms compared with existing numerical method.