A new analytical technique of the L-type difference schemes for time fractional mixed sub-diffusion and diffusion-wave equations

A time fractional mixed sub-diffusion and diffusion-wave equation involving at least two Caputo time derivatives of order gamma is an element of (1,2) and alpha is an element of (0, 1) is considered. A new analytical technique is introduced to analyze the standard finite difference method based on L1 scheme. Both stability and convergence of the scheme are proved rigorously. The final convergence result shows clearly that the temporal accuracy arrives at the order of O(tau(min{2-alpha,3-gamma})) in a discrete H-1-norm. This novel analytical technique can provide new insights in analyzing other multi-term mixed time fractional differential equations. (C) 2019 Elsevier Ltd. All rights reserved.