Department of Mathematics
Previously, based on the method of (radial powers) radial basis functions, we proposed a procedure for approximating derivative values from one-dimensional scattered noisy data. In this work, we show that the same approach also allows us to approximate the values of (Caputo) fractional derivatives (for orders between 0 and 1). With either an a priori or a posteriori strategy of choosing the regularization parameter, our convergence analysis shows that the approximated fractional derivative values converge at the same rate as in the case of integer order 1.
Fractional derivatives, inverse problem, convergence analysis, noisy data, regularization
Source Publication Title
Journal of Scientific Computing
Link to Publisher's Edition
Li, M., Wang, Y., & Ling, L. (2015). Numerical caputo differentiation by radial basis functions. Journal of Scientific Computing, 62 (1). https://doi.org/10.1007/s10915-014-9857-6