研究方向 |
分数阶微积分理论及其应用，主要是在扩散等可动边界问题（如药物控释系统）上的应用。该方向是分数阶微积分理论、流体力学、粘弹性材料、随机游走与反应扩散方程理论等数学和物理等其他学科知识的交叉，对实际问题建立模型，并且给出解析解、近似解或者数值解，综合运用了当代数学和物理中的各种理论和方法，是目前国际前沿课题之一。
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| 博士论文 |
Fractional
Moving Boundary Problems and Some of Its Applications to Controlled
Release System of Drug. [PDF] |
| 发表论文情况 |
1、Xicheng Li, Mingyu Xu, Shaowei Wang, Analytical solutions to the moving boundary problems with space-time-fractional derivatives in drug release devices, Journal of Physics A: Mathematical and Theoretical, 40 (2007) 12131-12141. [PDF] (SCI, 2008影响因子1.54) 2、Xicheng Li, Mingyu Xu, Shaowei Wang, Scale-invariant solutions to partial differential equations of fractional order with a moving boundary condition, Journal of Physics A: Mathematical and Theoretical, 41 (2008) 155202.[PDF] (SCI, 2008影响因子1.54) 3、Xicheng Li, Mingyu Xu, Xiaoyun Jiang, Homotopy perturbation method to time-fractional diffusion equation with a moving boundary，Applied Mathematics and Computation, 208 (2009) 434-439.[PDF] (SCI, 2008影响因子0.961) 4、Shaowei Wang, Mingyu Xu, Xicheng Li, Green’s function of time fractional diffusion equation and its applications in fractional quantum mechanics, Nonlinear Analysis, 10 (2009) 1081-1086. [PDF] (SCI, 2008影响因子1.778) 5、Xicheng Li, Mingyu Xu, A Model for reversible reaction in a sub-diffusive regime, Journal of Mathematical Physics, 50 (2009) 102708 . [PDF] (SCI, 2008影响因子1.085)
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