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Numerical approach of the nonlinear reaction-advection-diffusion equation with time-space conformable fractional derivatives.

Authors :
Brahim, Nouiri
Cakalli, Huseyin
Kocinac, Ljubisa D. R.
Ashyralyev, Allaberen
Harte, Robin
Dik, Mehmet
Canak, Ibrahim
Kandemir, Hacer Sengul
Tez, Mujgan
Gurtug, Ozay
Savas, Ekrem
Akay, Kadri Ulas
Ucgun, Filiz Cagatay
Uyaver, Sahin
Ashyralyyev, Charyyar
Sezer, Sefa Anil
Turkoglu, Arap Duran
Onvural, Oruc Raif
Sahin, Hakan
Source :
AIP Conference Proceedings; 2020, Vol. 2334 Issue 1, p1-5, 5p
Publication Year :
2020

Abstract

In this paper, a numerical approach is proposed for solving one dimensional nonlinear time-space-fractional reaction-advection-diffusion equation with Dirichlet boundary conditions. The fractional derivatives are described in the conformable sense. The numerical scheme is based on shifted Chebyshev polynomials of the fourth kind. The unknown function is written as Cheby-shev series with m terms. The nonlinear space fractional reaction-advection-diffusion equation is reduced to a system of nonlinear ordinary differential equations by using the properties of Chebyshev polynomials and conformable fractional calculus.The finite difference method is applied to solve this system. Finally, numerical example is presented to confirm the reliability and effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
0094243X
Volume :
2334
Issue :
1
Database :
Complementary Index
Journal :
AIP Conference Proceedings
Publication Type :
Conference
Accession number :
149021802
Full Text :
https://doi.org/10.1063/5.0042459