Integrated radial basis function technique to simulate the nonlinear system of time fractional distributed-order diffusion equation with graded time-mesh discretization

The distributed-order fractional calculus (DOFC) is a generalization of the fractional calculus which its application can be found in viscoelasticity, transport processes and control theory. In the current paper, a system of time fractional distributed-order diffusion equation is investigated, numerically. In the first stage, the time derivative is approximated by a finite difference formulation. The integral terms are approximated by the numerical integration. Then, a semi-discrete scheme is constructed by this procedure. In the second stage, The stability and convergence of the time-discrete outline are analyzed by the energy method. In the third stage, the space derivative is discretized by the compact integrated radial basis function (CLIRBF) as a truly meshless method. Also, the numerical procedures are performed on regular and irregular computational domains. The numerical experiments verify the ability, efficiency and accuracy of the developed numerical formulation.