WELL-POSEDNESS AND NUMERICAL ALGORITHM FOR THE TEMPERED FRACTIONAL DIFFERENTIAL EQUATIONS

被引:106
|
作者
Li, Can [1 ,2 ]
Deng, Weihua [3 ]
Zhao, Lijing [4 ]
机构
[1] Xian Univ Technol, Dept Appl Math, Xian 710048, Shaanxi, Peoples R China
[2] Beijing Computat Sci Res Ctr, Beijing 10084, Peoples R China
[3] Lanzhou Univ, Gansu Key Lab Appl Math & Complex Syst, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China
[4] Northwestern Polytech Univ, Dept Appl Math, Xian 710129, Shaanxi, Peoples R China
来源
基金
中国国家自然科学基金;
关键词
Tempered fractional operators; well-posedness; Jacobi-predictor-corrector algorithm; convergence; PREDICTOR-CORRECTOR APPROACH; DIFFUSION;
D O I
10.3934/dcdsb.2019026
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Trapped dynamics widely appears in nature, e.g., the motion of particles in viscous cytoplasm. The famous continuous time random walk (CTRW) model with power law waiting time distribution (having diverging first moment) describes this phenomenon. Because of the finite lifetime of biological particles, sometimes it is necessary to temper the power law measure such that the waiting time measure has convergent first moment. Then the time operator of the Fokker-Planck equation corresponding to the CTRW model with tempered waiting time measure is the so-called tempered fractional derivative. This paper focus on discussing the properties of the time tempered fractional derivative, and studying the well-posedness and the Jacobi-predictorcorrector algorithm for the tempered fractional ordinary differential equation. By adjusting the parameter of the proposed algorithm, high convergence order can be obtained and the computational cost linearly increases with time. The numerical results show that our algorithm converges with order N-I, where N-I is the number of interpolating points used in the scheme.
引用
收藏
页码:1989 / 2015
页数:27
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