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    Three-Variable Shifted Jacobi Polynomials Approach for Numerically Solving Three-Dimensional Multi-Term Fractional-Order PDEs with Variable Coefficients

    Jiaquan Xie1,3,*, Fuqiang Zhao1,3, Zhibin Yao1,3, Jun Zhang1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.115, No.1, pp. 67-84, 2018, DOI:10.3970/cmes.2018.115.067

    Abstract In this paper, the three-variable shifted Jacobi operational matrix of fractional derivatives is used together with the collocation method for numerical solution of three-dimensional multi-term fractional-order PDEs with variable coefficients. The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations which greatly simplifying the problem. The approximate solutions of nonlinear fractional PDEs with variable coefficients thus obtained by three-variable shifted Jacobi polynomials are compared with the exact solutions. Furthermore some theorems and lemmas are introduced to verify the convergence results of our algorithm. Lastly, More >

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