Abstract:

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.

Key words: Adomian decomposition method, Adomian polynomials, systems of integral equations of fractional order, convergence analysis, truncated error