THERMAL SCIENCE

International Scientific Journal

Rashid Nawaz

,

Rashid Ashraf

,

Laiq Zada

,

Hijaz Ahmad

,

Muhammad Farooq

,

Imtiaz Ahmad

,

Chutarat Tearnbucha

,

Weerawat Sudsutad

NEW APPROXIMATE SOLUTIONS TO TIME FRACTIONAL ORDER PARTIAL DIFFERENTIAL EQUATIONS OPTIMAL AUXILARY FUNCTION METHOD

ABSTRACT
In this article, approximate solutions of some PDE of fractional order are investi­gated with the help of a new semi-analytical method called the optimal auxiliary function method. The proposed method was tested upon the time-fractional Fisher equation, the time-fractional Fornberg-Whitham equation, and the time-fractional Inviscid Burger equation. The beauty of this method is that there is no need for discretization and assumptions of small or large parameters and provides an ap­proximate solution after only one iteration. The numerical results obtained by the proposed method compared with the other existing methods used in the literature. From the numerical and graphical results, it is clear that the proposed method gives a better solution than existing methods. The MATHEMATICA software pack­age has been used for the huge computational work.
KEYWORDS
optimal auxiliary function method, approximate solution, fractional order differential equations, Caputo’s derivative
PAPER SUBMITTED: 2023-02-15
PAPER REVISED: 2023-03-14
PAPER ACCEPTED: 2023-03-24
PUBLISHED ONLINE: 2023-04-08
DOI REFERENCE: https://doi.org/10.2298/TSCI23S1009N
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2023, VOLUME 27, ISSUE Special issue 1, PAGES [9 - 17]
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New approximate solutions to time fractional order partial differential equations optimal auxilary function method

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence