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

Document Type : Original Paper


1 Department of Applied Mathematics, Faculty of Mathematical Science, Shahrekord University, Shahrekord, P. O. Box 115, Iran.

2 Department of Mathematics, Payme Noor University, P. O. Box 19395-4697 Tehran, Iran.


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.


Main Subjects

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