Version 1
: Received: 20 May 2019 / Approved: 21 May 2019 / Online: 21 May 2019 (11:43:12 CEST)
How to cite:
Modanli, M. Using Difference Scheme Method to the Fractional Telegraph Model with Atangana-Baleanu-Caputo Derivative. Preprints2019, 2019050262. https://doi.org/10.20944/preprints201905.0262.v1.
Modanli, M. Using Difference Scheme Method to the Fractional Telegraph Model with Atangana-Baleanu-Caputo Derivative. Preprints 2019, 2019050262. https://doi.org/10.20944/preprints201905.0262.v1.
Cite as:
Modanli, M. Using Difference Scheme Method to the Fractional Telegraph Model with Atangana-Baleanu-Caputo Derivative. Preprints2019, 2019050262. https://doi.org/10.20944/preprints201905.0262.v1.
Modanli, M. Using Difference Scheme Method to the Fractional Telegraph Model with Atangana-Baleanu-Caputo Derivative. Preprints 2019, 2019050262. https://doi.org/10.20944/preprints201905.0262.v1.
Abstract
The fractional telegraph partial differential equationwith fractional Atangana-Baleanu-Caputo (ABC) derivative is studied. Laplacemethod is used to find the exact solution of this equation. Stabilityinequalities are proved for the exact solution. Difference schemes for theimplicit finite method are constructed. The implicit finite method is usedto deal with modelling the fractional telegraph differential equationdefined by Caputo fractional of Atangana-Baleanu (AB) derivative fordifferent interval. Stability of difference schemes for this problem isproved by the matrix method. Numerical results with respect to the exactsolution confirm the accuracy and effectiveness of the proposed method.
Keywords
fractional telegraph model with Atangana-Baleanu derivative; Laplace method; stability inequalites; difference schemes; implicit finite method
Subject
Computer Science and Mathematics, Computer Vision and Graphics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
