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Approximation solution of fractional partial differential equations by neural networks. (English) Zbl 1236.65110
Summary: Neural networks with radial basis functions (RBFs) method are used to solve a class of initial boundary value of fractional partial differential equations (PDEs) with variable coefficients on a finite domain. It takes the case where a left-handed or right-handed fractional spatial derivative may be present in the partial differential equations. Convergence of this method is discussed. A numerical example using neural networks RBF method for a two-sided fractional PDE also is presented and compared with other methods.

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
35R11 Fractional partial differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
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