Abstract: We discussed a class of  inverse problem of  time fractional order diffusion equations by using the fractional order Tikhonov regularization method. We gave selection criteria for the regularization parameter under  prior and posterior conditions, and gave rigorous  proofs of the convergence of the method. Numerical experimental results show that  the fractional order Tikhonov regularization method is effective in solving this problem.

Key words: fractional order inverse diffusion problem, fractional order Tikhonov regularization, selection rules for prior and posterior parameters, error estimates