中文摘要：

建立了含有外力的分数阶非线性对流-扩散方程．讨论了具有扩散系数D（x）∝x^-θ的整数阶方程，利用q-指数函数和q-对数函数的特性，求得了解析解．考虑吸附效应的分数阶方程，在非线性参量满足某种关系的情况下，求得了精确特解，并研究了解的渐近行为．

英文摘要：

Fractional nonlinear convection-diffusion equation with external forces is given. First, the integer equation is studied by considering the diffusion coefficient D（x） ∝ x^θ . By using the q-exponential function and q-logarithm function, the analytical solution of the equation is derived. Second, a fractional equation with absorption is analyzed. On condition that the nonlinear pa- rameters satisfy certain relationships, a special solution can be obtained. In addition, the asymptotic behaviors for the solution are also discussed.