Distributed order Gauss-Quadrature scheme for distributed order fractional sub-diffusion model

Abstract

In this manuscript, our goal is to design distributed order Gauss-Quadrature scheme for solving distributed order fractional sub-diffusion mathematical model based on an orthogonal generating polynomial (OGP) with respect to the weight function of distributed order anomalous time-fractional subdiffusion partial differential equation (DOT-FSPDE). Based on OGP we established a new computational algorithm for the DOT-FSPDE, which is controlled by the single input distribution weight function of DOT-FSPDE. The proposed problem has been solved numerically with the help of the OGP-Gauss quadrature rule along with an operational matrix based on the designed OGP technique. Also, we established error bounds, convergence analysis, numerical algorithms, error estimation, numerical stability and theoretical stability analysis of the designed scheme. There are several test examples which have been solved for the reliability of the proposed computational method with less CPU time. The proposed technique was found to be more accurate in comparison with the existing scheme.