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We consider a class of a generalized time-fractional telegraph equations. The existence of a weak solution of the corresponding initial-boundary value problem has been proved. A finite difference scheme approximating the problem is proposed, and its stability is proved. An estimate for the rate of convergence, in special discrete energetic Sobolev’s norm, is obtained. The theoretical results are confirmed by numerical examples.

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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.

In this paper an initial-boundary value problem for fractional in time diffusion-wave equation is considered. A priori estimates in Sobolev spaces are derived. A fully discrete difference scheme approximating the problem is proposed and its stability and convergence are investigated. A numerical example demonstrates the theoretical results. [Projekat Ministarstva nauke Republike Srbije, br. 174015]