Model Order Reduction for the Problems with Fractional Order Differential Operators
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Model reduction techniques can be used in order to find the numerical solutions of PDEs depending on parameters (pPDE). These parameters are proposed as a vector. In this talk we consider pPDE variant of a boundary value problem with Riemann-Liouville fractional derivative. We aim to propose Reduce Basis (RB) Method via Greedy algorithm for the corresponding parametrized fractional problem. To this end we first prove the wellposedness of the solutions in an appropriate Sobolev space with fractional order. Then several numerical experiments are presented in order to investigate the convergence of the numerical solutions and discuss the RB for a fixed value of fractional derivative order.