In this talk, we present the local discontinuous Galerkin (LDG) finite element methods for three kinds of Caputo-type partial differential equations (PDEs): reaction-diffusion equation, reaction-diffusion-wave equation, and cable equation; and we introduce the DG finite element methods for Caputo-type nonlinear conservation law. Stability and convergence are displayed. And numerical examples are also included which support the theoretical analysis.

Changpin Li earned his Ph D in computational mathematics from Shanghai University. After graduation, he worked in the same university. He has ever been the director of Institute of Computational Mathematics in Shanghai University. His present research interests include: numerical methods and scientific computations of fractional partial differential equations, dynamics of fractional differential equations. He has published more than 90 papers in referred journals, edited one book and published one book which have been published in World Scientific and CRC Press, respectively. He was awarded the Shanghai Natural Science Prize in 2010 and 2017, Bao Steel Prize in 2011, Riemann-Liouville Award: Best FDA Paper (theory) in FDA’12 in 2012.