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In this paper we consider finite-difference scheme for a fractional  super-diffusion equation with the coefficient at the time derivative containing Dirac delta distribution. The stability and convergence of the scheme are proven using the discrete energy method. Estimate for the rate of the convergence compatible with the smoothness of the solution is obtained. A numerical exampledemonstrates the theoretical results.

mathematical modelling, super-diffusion, fractional in time diffusion-wave equation, interface problems