Approximations for the Caputo derivative (II)
Numerical Analysis
2018-08-28 v2
Abstract
In the present paper we use the expansion formula of the polylogarithm function to construct approximations of the Caputo derivative which are related to the midpoint approximation of the integral in the definition of the Caputo derivative. The asymptotic expansion formula of the Riemann sum approximation of the beta function and the first terms of the expansion formulas of the approximations of the Caputo derivative of the power function are obtained in the paper. The induced shifted approximations of the Gr\"unwald formula and the approximations of the Caputo derivative studied in the first part of the paper are constructed and applied for numerical solution of fractional differential equations.
Keywords
Cite
@article{arxiv.1604.07188,
title = {Approximations for the Caputo derivative (II)},
author = {Yuri Dimitrov and Venelin Todorov and Radan Miryanov},
journal= {arXiv preprint arXiv:1604.07188},
year = {2018}
}