Numerical solution of variable order fractional differential equations
Abstract
A method for the numerical solution of variable order (VO) fractional differential equations (FDE) is presented. The method applies to linear as well as to nonlinear VO-FDEs. The Caputo type VO fractional derivative is employed. First, an simple expression, which approximates the VO fractional derivative, is established and then a procedure based on this approximation is developed to solve VO-FDEs linear and nonlinear, both explicit and implicit. VO-FDEs with variable coefficients are also treated. The method is illustrated by solving the second order VO-FDE describing the response of the VO fractional oscillator, linear and nonlinear (Duffing). However, it can be straightforwardly extended to higher order VO-FDEs. The presented method, in addition to its effectiveness, is simple to implement and program on a computer. The obtained results validate the efficiency and accuracy of the developed method
Cite
@article{arxiv.1802.00519,
title = {Numerical solution of variable order fractional differential equations},
author = {John T. Katsikadelis},
journal= {arXiv preprint arXiv:1802.00519},
year = {2018}
}
Comments
15 pages, 12 figures, 1 Table