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We consider the time fractional wave equation with coefficient which contains the Dirac delta distribution. The existence of generalized solutions of this initial-boundary value problem is proved. An implicit finite difference scheme approximating the problem is developed and its stability is proved. Estimates for the rate of convergence in special discrete energetic Sobolev norms are obtained. A numerical example confirms the theoretical results.

Finite Difference Approximation of Fractional Wave Equation with Concentrated Capacity