Abstract: We use the modified Adomian decomposition method(ADM) for solving the nonlinear fractional boundary value problem {D(α0) + u(x) = f(x, u(x)), 0 < x < 1, 3 < α≤ 4 u(0) = α0, u’’ (0) = α2 u(1) = β0, u’’(1) = β2} (1) where D(0α)+u is Caputo fractional derivative and α0, α2, β0, β2 is not zero at all, and f:[0,1]×R→ R is continuous. The calculated numerical results show reliability and efficiency of the algorithm given. The numerical procedure is tested on linear and nonlinear problems. 

Key words: Caputo fractional derivative, Adomian decomposition method, differential equations