报告题目:Fractional calculus and its applications

报告人：刘建根 教授（常熟理工学院）

报告时间：2024年03月22日 周五 下午15:20---16:20

报告地点：屏峰校区 广A216

摘要：This report first introduces the development process of fractional calculus. Then it is used to the time fractional KdV type equation in the sense of the Riemann-Liouville fractional derivative. The Korteweg-de Vries equation is an essential model to characterize shallow water waves in fluid mechanics. At the beginning of, we applied the fractional Lie symmetry scheme to derive their symmetry. We found that the vector fields of these considered equations decrease as the independent variables. Subsequently, the one-parameter Lie transformations group of these concerned models are yielded. At the same time, they can be reduced into fractional order ordinary differential equations with the Erdlyi-Kober fractional operators. Finally, by obtaining the nonlinear self-adjointness, conservation laws of the generalized time fractional KdV equation were also found. These good results provide a basis for us to further understand the phenomenon of shallow water waves.

报告人简介：刘建根，常熟理工学院，教授，主要从事孤立子与可积系统理论和分数阶微分方程理论等方面的研究。在《Acta Mathematica Scientia》、《Journal of Geometry and Physics》、《Chaos, Solitons & Fractals》、《Fractals》和《International Journal of Mathematics》等国际知名期刊公开发表学术论文三十余篇，参与国家级项目1项，主持省级，厅级项目4项。担任Journal of Physics A: Mathematical and Theoretical、Applied Numerical Mathematics、Numerical Methods for Partial Differential Equations、Nonlinear Dynamics和Chaos, Solitons & Fractals等SCI学术期刊特邀审稿人。

邀请人：任 博