@article{Chen2022, 
author = {Yumei Chen and Jiajie Zhang and Chao Pan},
title = {Numerical approximation of a variable-order time fractional advection-reaction-diffusion model via shifted Gegenbauer polynomials},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {8},
pages = {15612-15632},
keywords = {advection-reaction-diffusion equation, variable-order time fractional derivative, Atangana-Baleanu-Caputo derivative, shifted Gegenbauer cardinal function, spectral collocation method},
url = {https://www.sciopen.com/article/10.3934/math.2022855},
doi = {10.3934/math.2022855},
abstract = {The fractional advection-reaction-diffusion equation plays a key role in describing the processes of multiple species transported by a fluid. Different numerical methods have been proposed for the case of fixed-order derivatives, while there are no such methods for the generalization of variable-order cases. In this paper, a numerical treatment is given to solve a variable-order model with time fractional derivative defined in the Atangana-Baleanu-Caputo sense. By using shifted Gegenbauer cardinal function, this approach is based on the application of spectral collocation method and operator matrices. Then the desired problem is transformed into solving a nonlinear system, which can greatly simplifies the solution process. Numerical experiments are presented to illustrate the effectiveness and accuracy of the proposed method.}
}