A numerical evaluation and regularization of Caputo fractional derivatives

作者：Li, Ming^*; Xiong, X. T.; Wang, Y. J.

来源：5th International Conference on Inverse Problems, City Univ Hong Kong, Hong Kong, JAPAN, 2010-12-13 to 2010-12-17.

DOI：10.1088/1742-6596/290/1/012011

• Numerical derivatives
• fractional derivatives
• ill-posed
• regularization

Numerical evaluations of Caputo fractional derivatives for scattered noisy data is an important problem in scientific research and practical applications. Fractional derivatives have been applied recently to the numerical solution of problems in fluid and continuum mechanics. The Caputo fractional derivative of order a is given as follows
f((alpha))(t) = 1/Gamma(1-alpha) integral(t)(0)f((n))(s)/(t - s)(alpha)ds, 0The above definition includes a Volterra integral equation with weakly singular kernels and difficult to calculate. In this paper, a faster convergence numerical schedule is given and applied to solve several fractional-diffusion heat conduction problems. Convergence rates of interest are also presented here. Several numerical results are given to show the effectiveness of the proposed numerical schedule.

• 出版日期2011
• 单位太原理工大学; 西北师范大学