中文摘要：

通过Adomian分解法求解非线性分数阶Volterra积分方程组的数值解.将多元Adomian多项式与分数阶积分定义有效结合,得到了Adomian级数解;结合Laplace变换讨论级数解的收敛性,证明了所得级数解收敛于精确解,并给出最大绝对截断误差.数值算例表明,该方法可行、有效.

英文摘要：

During solving the numerical solution of systems of nonliner Volterra integral equations of fractional order by the Adomian decomposition method,the Adomian series solution was obtained by combining the multivariable Adomian polynomials with the definition of fractional order integral.At the same time,the convergence of the series solution was discussed with the help of Laplace transform.It was shown that the series solution converged to the exact solution.And the maximum absolute truncated error of the Adomian series solution was also given.Finally,effectiveness and feasibility of the proposed Adomian decomposition method were shown by numerical example.