Abstract: In this paper, it proposes a simple and efficient perturbative approach which is based on homotopy perturbation theory and Sumudu transform method, for solving Jumarie’s modified Riemann-Liouville（R-L）fractional equation with fractional initial conditions. However, nearly all the previous works avoid the term of fractional initial conditions. The results show the high accuracy, simplicity and efficiency of the technique.

Key words: Jumarie’s modified R-L fractional derivative, Sumudu transform, homotopy perturbation method, approximate solution

摘要： 结合同伦摄动理论和Sumudu变换方法，提出了一种简单有效的摄动方法，并应用该方法求解了Jumarie’s修正的Riemann-Liouville（R-L）分数阶的方程，该方程带有分数阶的初值条件，而以前的文献中很少讨论分数阶的初值条件。结果表明该方法具有较高的精度和有效性。

关键词: Jumarie&rsquo, s修正的R-L分数阶导数, Sumudu变换, 同伦扰动法, 近似解