Preprint Article Version 1 This version is not peer-reviewed

Using Difference Scheme Method to the Fractional Telegraph Model with Atangana-Baleanu-Caputo Derivative

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. Preprints 2019, 2019050262 (doi: 10.20944/preprints201905.0262.v1). Modanli, M. Using Difference Scheme Method to the Fractional Telegraph Model with Atangana-Baleanu-Caputo Derivative. Preprints 2019, 2019050262 (doi: 10.20944/preprints201905.0262.v1).

Abstract

The fractional telegraph partial differential equation with fractional Atangana-Baleanu-Caputo (ABC) derivative is studied. Laplace method is used to find the exact solution of this equation. Stability inequalities are proved for the exact solution. Difference schemes for the implicit finite method are constructed. The implicit finite method is used to deal with modelling the fractional telegraph differential equation defined by Caputo fractional of Atangana-Baleanu (AB) derivative for different interval. Stability of difference schemes for this problem is proved by the matrix method. Numerical results with respect to the exact solution confirm the accuracy and effectiveness of the proposed method.

Subject Areas

fractional telegraph model with Atangana-Baleanu derivative; Laplace method; stability inequalites; difference schemes; implicit finite method

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