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中文摘要：
考虑一般的对流扩散方程，将一阶的时间导数用 Caputo 分数阶导数替换，二阶的空间导数用 Riemann-Liouville分数阶导数替换，得到了一个 Riemann-Liouville-Caputo分数阶对流扩散方程.给出了这个方程的一种计算有效的隐式差分格式，并证明了该差分格式是无条件稳定、无条件收敛的，其收敛阶为（）Oτ＋h.最后给出了数值例子.
英文摘要：
A classical convection-dispersion equation in which the first-order time derivative was replaced by a Caputo derivative and the second-order space derivative was replaced by a Riemann-Liouville derivative was considered, and a Riemann-Liouville-Caputo fractional convection-dispersion equation was obtained. A computationally effective implicit difference approximation was presented. It was shown that the scheme was unconditionally stable and convergent respectively. The convergence order of the scheme was （ ）Oτ＋h . Finally, some numerical examples were given.
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