Numerical investigation and error estimate for multi-term time-fractional diffusion equations based on new fractional operator

In this paper‎, ‎a numerical method is provided for solving multi-term time-fractional diffusion equations associated with a new fractional operator‎. ‎A semi-discrete scheme is obtained in temporal direction based on the finite difference method afterwards‎, ‎a Chebyshev-spectral method is used for spatial discretization‎. ‎Also‎, ‎the stability and error analysis are investigated‎. ‎Moreover‎, ‎the multi-term time-fractional diffusion equation is extended to a distributed order diffusion equation and numerical analysis has been done on it‎. ‎Finally‎, ‎the theoretical results are confirmed using some numerical examples.