Multistep Approach for Nonlinear Fractional Bloch System Using Adomian Decomposition Techniques

Asad Freihat; Shatha Hasan; Mohammed Al-Smadi; Omar Abu Arqub; Shaher Momani

doi:10.1007/978-981-15-0430-3_9

Multistep Approach for Nonlinear Fractional Bloch System Using Adomian Decomposition Techniques

Asad Freihat
, Shatha Hasan
, Mohammed Al-Smadi
, Omar Abu Arqub
, Shaher Momani

Nonlinear Dynamic Research Centre (NDRC)

Al-Balqa Applied University
University of Jordan

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

In this chapter, a superb multistep approach, based on the Adomian decomposition method (ADM), is successfully implemented for solving nonlinear fractional Bolch system over a vast interval, numerically. This approach is demonstrated by studying the dynamical behavior of the fractional Bolch equations (FBEs) at different values of fractional order in the sense of Caputo concept over a sequence of the considerable domain. Further, the numerical comparison between the proposed approach and implicit Runge–Kutta method is discussed by providing an illustrated example. The gained results reveal that the MADM is a systematic technique in obtaining a feasible solution for many nonlinear systems of fractional order arising in natural sciences.

Original language	English
Title of host publication	Fractional Calculus - ICFDA 2018
Editors	Praveen Agarwal, Praveen Agarwal, Praveen Agarwal, Dumitru Baleanu, YangQuan Chen, Shaher Momani, José António Tenreiro Machado
Publisher	Springer
Pages	153-171
Number of pages	19
ISBN (Print)	9789811504297
DOIs	https://doi.org/10.1007/978-981-15-0430-3_9
State	Published - 2019
Event	International Conference on Fractional Differentiation and its Applications, ICFDA 2018 - Amman, Jordan Duration: 16 Jul 2018 → 18 Jul 2018

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	303
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	International Conference on Fractional Differentiation and its Applications, ICFDA 2018
Country/Territory	Jordan
City	Amman
Period	16/07/18 → 18/07/18

Keywords

Adomian decomposition method
Bolch equations
Fractional system
Multistep approach

Access to Document

10.1007/978-981-15-0430-3_9

Cite this

Freihat, A., Hasan, S., Al-Smadi, M., Arqub, O. A., & Momani, S. (2019). Multistep Approach for Nonlinear Fractional Bloch System Using Adomian Decomposition Techniques. In P. Agarwal, P. Agarwal, P. Agarwal, D. Baleanu, Y. Chen, S. Momani, & J. A. T. Machado (Eds.), Fractional Calculus - ICFDA 2018 (pp. 153-171). (Springer Proceedings in Mathematics and Statistics; Vol. 303). Springer. https://doi.org/10.1007/978-981-15-0430-3_9

Freihat, Asad ; Hasan, Shatha ; Al-Smadi, Mohammed et al. / Multistep Approach for Nonlinear Fractional Bloch System Using Adomian Decomposition Techniques. Fractional Calculus - ICFDA 2018. editor / Praveen Agarwal ; Praveen Agarwal ; Praveen Agarwal ; Dumitru Baleanu ; YangQuan Chen ; Shaher Momani ; José António Tenreiro Machado. Springer, 2019. pp. 153-171 (Springer Proceedings in Mathematics and Statistics).

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title = "Multistep Approach for Nonlinear Fractional Bloch System Using Adomian Decomposition Techniques",

abstract = "In this chapter, a superb multistep approach, based on the Adomian decomposition method (ADM), is successfully implemented for solving nonlinear fractional Bolch system over a vast interval, numerically. This approach is demonstrated by studying the dynamical behavior of the fractional Bolch equations (FBEs) at different values of fractional order in the sense of Caputo concept over a sequence of the considerable domain. Further, the numerical comparison between the proposed approach and implicit Runge–Kutta method is discussed by providing an illustrated example. The gained results reveal that the MADM is a systematic technique in obtaining a feasible solution for many nonlinear systems of fractional order arising in natural sciences.",

keywords = "Adomian decomposition method, Bolch equations, Fractional system, Multistep approach",

author = "Asad Freihat and Shatha Hasan and Mohammed Al-Smadi and Arqub, \{Omar Abu\} and Shaher Momani",

note = "Publisher Copyright: {\textcopyright} 2019, Springer Nature Singapore Pte Ltd.; International Conference on Fractional Differentiation and its Applications, ICFDA 2018 ; Conference date: 16-07-2018 Through 18-07-2018",

year = "2019",

doi = "10.1007/978-981-15-0430-3\_9",

language = "English",

isbn = "9789811504297",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer",

pages = "153--171",

editor = "Praveen Agarwal and Praveen Agarwal and Praveen Agarwal and Dumitru Baleanu and YangQuan Chen and Shaher Momani and Machado, \{Jos{\'e} Ant{\'o}nio Tenreiro\}",

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Freihat, A, Hasan, S, Al-Smadi, M, Arqub, OA & Momani, S 2019, Multistep Approach for Nonlinear Fractional Bloch System Using Adomian Decomposition Techniques. in P Agarwal, P Agarwal, P Agarwal, D Baleanu, Y Chen, S Momani & JAT Machado (eds), Fractional Calculus - ICFDA 2018. Springer Proceedings in Mathematics and Statistics, vol. 303, Springer, pp. 153-171, International Conference on Fractional Differentiation and its Applications, ICFDA 2018, Amman, Jordan, 16/07/18. https://doi.org/10.1007/978-981-15-0430-3_9

Multistep Approach for Nonlinear Fractional Bloch System Using Adomian Decomposition Techniques. / Freihat, Asad; Hasan, Shatha; Al-Smadi, Mohammed et al.
Fractional Calculus - ICFDA 2018. ed. / Praveen Agarwal; Praveen Agarwal; Praveen Agarwal; Dumitru Baleanu; YangQuan Chen; Shaher Momani; José António Tenreiro Machado. Springer, 2019. p. 153-171 (Springer Proceedings in Mathematics and Statistics; Vol. 303).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T1 - Multistep Approach for Nonlinear Fractional Bloch System Using Adomian Decomposition Techniques

AU - Freihat, Asad

AU - Hasan, Shatha

AU - Al-Smadi, Mohammed

AU - Arqub, Omar Abu

AU - Momani, Shaher

PY - 2019

Y1 - 2019

N2 - In this chapter, a superb multistep approach, based on the Adomian decomposition method (ADM), is successfully implemented for solving nonlinear fractional Bolch system over a vast interval, numerically. This approach is demonstrated by studying the dynamical behavior of the fractional Bolch equations (FBEs) at different values of fractional order in the sense of Caputo concept over a sequence of the considerable domain. Further, the numerical comparison between the proposed approach and implicit Runge–Kutta method is discussed by providing an illustrated example. The gained results reveal that the MADM is a systematic technique in obtaining a feasible solution for many nonlinear systems of fractional order arising in natural sciences.

AB - In this chapter, a superb multistep approach, based on the Adomian decomposition method (ADM), is successfully implemented for solving nonlinear fractional Bolch system over a vast interval, numerically. This approach is demonstrated by studying the dynamical behavior of the fractional Bolch equations (FBEs) at different values of fractional order in the sense of Caputo concept over a sequence of the considerable domain. Further, the numerical comparison between the proposed approach and implicit Runge–Kutta method is discussed by providing an illustrated example. The gained results reveal that the MADM is a systematic technique in obtaining a feasible solution for many nonlinear systems of fractional order arising in natural sciences.

KW - Adomian decomposition method

KW - Bolch equations

KW - Fractional system

KW - Multistep approach

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BT - Fractional Calculus - ICFDA 2018

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A2 - Baleanu, Dumitru

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Freihat A, Hasan S, Al-Smadi M, Arqub OA, Momani S. Multistep Approach for Nonlinear Fractional Bloch System Using Adomian Decomposition Techniques. In Agarwal P, Agarwal P, Agarwal P, Baleanu D, Chen Y, Momani S, Machado JAT, editors, Fractional Calculus - ICFDA 2018. Springer. 2019. p. 153-171. (Springer Proceedings in Mathematics and Statistics). doi: 10.1007/978-981-15-0430-3_9

Multistep Approach for Nonlinear Fractional Bloch System Using Adomian Decomposition Techniques

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