A novel solution to the fraction chaotic Chen system is presented in this paper by using the step homotopy analysis method. This method yields a continuous solution in terms of a rapidly convergent infinite power series with easily computable terms. Moreover, the residual error of the SHAM solution is defined and computed for each time interval. Via the computing of the residual error we observe that the accuracy of the present method tends to 10 −11 which is very high. c ⃝2015 All rights

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... ed. where Γ(α) is the well-known gamma function. Some of the properties of the operator J α , which we will need here, are as follows: For f ∈ C µ , µ ≥ −1, α, β ≥ 0 and γ ≥ −1: 3. J α t γ = Γ(γ+1) Γ(α+γ+1) t α+γ .