A numerical method for solving variable-order time fractional differential equations is developed by using two-dimensional fractional-order Legendre wavelets(FOLWs).In the sense of Riemann-Liouville(R-L)variable fractional-order integral,the variable fractional-order integral formulas of FOLWs are derived by means of unit step function and regularized β function.Based on the generalized fractional-order Taylor expansion,the error estimation of two-dimensional FOLWs expansion is studied.The variable-order time fractional differential equation is discretized into a system of algebraic equation by using the collocation method.The resulted linear and nonlinear system are solved by Gauss elimination method and Picard iterative method,respectively.The effectiveness,applicability and accuracy of the proposed method are verified by several numerical examples.
维普
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