| Abstract: |
| In this report we consider initial-boundary value problems for a hyperbolic equation (with a fractional time Caputo derivative):
$$D_{0t}^{\alpha} u(x,t) - u_{xx}(x,t) + q(x)u(x,t) = f(x,t), \ 1 0.$$
In the case when the boundary conditions are strongly regular, the system of root vectors of this spectral problem forms a Riesz basis in \(L_2(0,1)\). The Fourier method can be implemented to solve the original problem.
However, when the boundary conditions are non strongly regular, the system of root vectors of the spectral problem may not form an unconditional basis, preventing the use of the Fourier method. These are the types of problems that will be presented in this report. |
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