AccScience Publishing / IJOCTA / Volume 9 / Issue 3 / DOI: 10.11121/ijocta.01.2019.00678
RESEARCH ARTICLE

On the numerical solution for third order fractional partial differential equation by difference scheme method

Mahmut Modanlı1*
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1 Harran University, Faculty of Art and Science, Department of Mathematics, Turkey
Submitted: 15 August 2018 | Accepted: 10 December 2018 | Published: 19 March 2019
© 2019 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
Abstract

The exact solution of third order fractional partial differential equations is obtained depending on initial-boundary value problem. The exact solutions and theorem of stability estimates is presented for this equation. Difference schemes are constructed for finite difference scheme. The stability of these difference schemes for this problem are given. Using of these methods, numerical solutions of the third order fractional partial differential equation defined by Caputo fractional derivative for fractional orders ?=0.1, 0.5, 0.9 are calculated. Numerical results are compared with the exact solution and the accuracy and effectiveness of the proposed methods are investigated.

Keywords
Third order fractional partial differential equations
Exact solutions
Stability estimates
Difference schemes
Conflict of interest
The authors declare they have no competing interests.
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