An extension of the concept of the asymptotic expansions method is presented in this paper.
The multi-order differential equations of fractional order are investigated and the convergence of
the proposed method is proven. The reported results show that the present approach
is very effective and accurate and also are in good agreement with the ones in the literature.
Key Words: Asymptotic expansion, Caputo derivative, convergence analysis.
2000 Mathematics Subject Classification: Primary: 41A58;
Secondary: 39A10, 34K28, 41A10.