Numerical study for two types variable-order Burgers' equations with proportional delay

Abstract

In this paper, variable order Burgers' equations with proportional delays in time and space are studied. The variable order derivatives are defined in the sense of Atangana and Baleanu. Two types of variable order Atangana and Baleanu definitions are presented here. The nonstandard weighted average finite difference method is developed to study numerically the proposed models problem in one and two dimensional. Moreover, the stability analysis and truncation error are analyzed. Two test examples with proportional delays are given to characterizing the memory property of the proposed models. It is found that the proposed technique can be applied to study such variable-order fractional equations simply and effectively.