Open Access

ARTICLE

An Efficient Computational Method for Differential Equations of Fractional Type

by Mustafa Turkyilmazoglu^1,2,*

1 Department of Mathematics, Hacettepe University, Ankara, 06532, Turkey
2 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40447, Taiwan

* Corresponding Author: Mustafa Turkyilmazoglu. Email:

Computer Modeling in Engineering & Sciences 2022, 133(1), 47-65. https://doi.org/10.32604/cmes.2022.020781

Received 11 December 2021; Accepted 22 February 2022; Issue published 18 July 2022

Abstract

An effective solution method of fractional ordinary and partial differential equations is proposed in the present paper. The standard Adomian Decomposition Method (ADM) is modified via introducing a functional term involving both a variable and a parameter. A residual approach is then adopted to identify the optimal value of the embedded parameter within the frame of L² norm. Numerical experiments on sample problems of open literature prove that the presented algorithm is quite accurate, more advantageous over the traditional ADM and straightforward to implement for the fractional ordinary and partial differential equations of the recent focus of mathematical models. Better performance of the method is further evidenced against some compared commonly used numerical techniques.

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Keywords

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