The numerical solution of high dimensional variable-order time fractional diffusion equation via the singular boundary method

•The 3D variable-order time fractional variable-order time fractional diffusion is generated.•An efficient meshless method is proposed for numerical solution of the new problem.•The proposed approach is established upon the singular boundary method.•The method accuracy is examined by some numerical examples on various geometries.•The method can be extended for other types of variable-order fractional problems.