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A note on the fractional hyperbolic differential and difference equations. (English) Zbl 1221.65212

The paper presents a first order difference scheme applied on an hyperbolic boundary value problem with a fractional differential equation with a self-adjoint operator \(A(t)\) formulated in a Hilbert space \(H\). The stability estimates for the solution of the difference scheme are shown.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L10 Second-order hyperbolic equations
35R11 Fractional partial differential equations
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