Numerical analysis of coupled fractional differential equations with Atangana-Baleanu fractional derivative

Ilknur Koca

doi:10.3934/dcdss.2019031

Article Contents

2019, Volume 12, Issue 3: 475-486. Doi: 10.3934/dcdss.2019031

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Numerical analysis of coupled fractional differential equations with Atangana-Baleanu fractional derivative

Ilknur Koca

Mehmet Akif Ersoy University, Department of Mathematics, Faculty of Sciences, 15100, Burdur, Turkey

Received: June 2017

Revised: September 2017

Published: October 2018

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Abstract

A nonlinear system of two fractional nonlinear differential equations with Atangana-Baleanu derivative is considered in this work. General conditions under which a system solution exists and unique are presented using the fixed-point theorem method. The well-established numerical scheme is used to solve the system of equations. A numerical analysis is presented to secure the stability and convergence of the used numerical scheme.

Keywords:

Non-linear equations,
existence and uniqueness,
Atangana-Baleanu fractional differentiation,
numerical analysis.

Mathematics Subject Classification: Primary: 34A34, 34A12, 34A08; Secondary: 47N40.

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