### Journals Information

Mathematics and Statistics Vol. 9(6), pp. 976 - 983
DOI: 10.13189/ms.2021.090613
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## Combined Adomian Decomposition Method with Integral Transform

Betty Subartini 1,*, Ira Sumiati 2, Sukono 1, Riaman 1, Ibrahim Mohammed Sulaiman 3
1 Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Jl. Raya Bandung Sumedang KM.21, Hegarmanah, Jatinangor, Sumedang Regency, West Java 45363, Indonesia
2 Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Jl. Raya Bandung Sumedang KM.21, Hegarmanah, Jatinangor, Sumedang Regency, West Java 45363, Indonesia
3 Department of Mathematics and Statistics, School of Quantitative Sciences, Universiti Utara Malaysia, Sintok, Malaysia

ABSTRACT

At present, three numerical solution methods have mainly been used to solve fractional-order chaotic systems in the literature: frequency domain approximation, predictor–corrector approach and Adomian decomposition method (ADM). Based on the literature, ADM is capable of dealing with linear and nonlinear problems in a time domain. Also, the Adomian decomposition method (ADM) is among the efficient approaches for solving linear and non-linear equations. Numerical solution method is one of the critical problems in theoretical research and in the applications of fractional-order systems. The solution is decomposed into an infinite series and the integral transformation to a differential equation is implemented in this work. Furthermore, the solution can be thought of as an infinite series that converges to an exact solution. The aim of this study is to combine the Adomian decomposition approach with a different integral transformation, including Laplace, Sumudu, Natural, Elzaki, Mohand, and Kashuri-Fundo. The study's key finding is that employing the combined method to solve fractional ordinary differential equations yields good results. The main contribution of our study shows that the combined numerical methods considered produce excellent numerical performance for solving fractional ordinary differential equations. Therefore, the proposed combined method has practical implications in solving fractional order differential equations in science and social sciences, such as finding analytical and numerical solutions for secure communication system, biological system, financial risk models, physics phenomenon, neuron models and engineering application.

KEYWORDS
Adomian Decomposition Method, Natural Transform, Sumudu Transform, Laplace Transform, Elzaki Transform, Mohand Transform, Khasuri-Fundo Transform

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Betty Subartini , Ira Sumiati , Sukono , Riaman , Ibrahim Mohammed Sulaiman , "Combined Adomian Decomposition Method with Integral Transform," Mathematics and Statistics, Vol. 9, No. 6, pp. 976 - 983, 2021. DOI: 10.13189/ms.2021.090613.

(b). APA Format:
Betty Subartini , Ira Sumiati , Sukono , Riaman , Ibrahim Mohammed Sulaiman (2021). Combined Adomian Decomposition Method with Integral Transform. Mathematics and Statistics, 9(6), 976 - 983. DOI: 10.13189/ms.2021.090613.