A finite difference scheme for time-space fractional distributed-order diffusion eqations with weakly ‎singular ‎solutions

‎In this paper‎, ‎the time-space distributed-order fractional diffusion equations with weakly singular solutions are considered‎. We provide the difference scheme using a nonuniform mesh to solve ‎equations‎‎. ‎The stability and convergence of the difference scheme are discussed‎, ‎We prove that the difference scheme is unconditionally stable‎. ‎We find that the difference scheme is convergent‎. ‎We also show that the temporal convergence order on the nonuniform mesh is higher than on the uniform mesh‎. Finally, some numerical examples are given to verify the theoretical analysis‏.