Chebyshev polynomials approach for numerically solving system of two-dimensional fractional PDEs and convergence analysis

In this paper, an efficient numerical technique based on the Chebsyhev orthogonal polynomials is established to obtain the approximate solutions of system of two-dimensional fractional-order PDEs with initial conditions. We construct the corresponding differential operational matrix of fractional-order, and then transform the problem into a system of linear algebra equations. Compared with other analytical or semi-analytical methods, ours can achieve better convergence accuracy only small terms are expanded. Moreover the proposed algorithm is simple in theoretical derivation and numerical simulation. In our study, the convergence analysis of the system is emphatically investigated than other numerical approaches. Lastly, three numerical examples are applied to test the algorithm and that the obtained numerical results show that our approach is effective and robust.

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