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In this paper, we discuss the existence and uniqueness of solutions for a class of integral boundary value problems of nonlinear multi-term fractional differential equations and propose a new method to obtain their approximate solutions. The existence results are established by the Banach fixed point theorem, and approximate solutions are determined by the Daftardar-Gejji and Jafari iterative method (DJIM) and the Adomian decomposition method (ADM). Finally, we present some examples to illustrate the existence result and the effectiveness of applied approximate techniques.