We present an effective practical approach for solving multi-order nonlinear fractional differential equations. Our method uses integrated Bernoulli polynomials and comes with a comprehensive convergence analysis. The integrated Bernoulli polynomials are combined with the collocation and simple iteration methods to approximate the solutions. We have provided several numerical examples to demonstrate the effectiveness, strength, and flexibility of our method. The results obtained from implementing the method have been compared with exact solutions and results obtained from other methods mentioned in the articles.
