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Multistep Approach for Nonlinear Fractional Bloch System Using Adomian Decomposition Techniques

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Fractional Calculus (ICFDA 2018)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 303))

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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 \(\alpha \) 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.

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Author information

Authors and Affiliations

  1. Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun, 26816, Jordan

    Asad Freihat, Shatha Hasan & Mohammed Al-Smadi

  2. Department of Mathematics, Faculty of Science, Jordan University, Amman, 11942, Jordan

    Omar Abu Arqub & Shaher Momani

  3. Department of Mathematics and Sciences, College of Humanities and Sciences, Ajman University, Ajman, UAE

    Shaher Momani

Authors
  1. Asad Freihat
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  2. Shatha Hasan
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  3. Mohammed Al-Smadi
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  4. Omar Abu Arqub
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  5. Shaher Momani
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Corresponding author

Correspondence to Shaher Momani .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Anand International College of Engineering, Jaipur, Rajasthan, India

    Praveen Agarwal

  2. Department of Mathematics and Computer Science, Çankaya University, Ankara, Turkey

    Dumitru Baleanu

  3. School of Engineering (MESA Lab), University of California, Merced, Merced, CA, USA

    YangQuan Chen

  4. Department of Mathematics, The University of Jordan, Amman, Jordan

    Shaher Momani

  5. Institute of Engineering, Polytechnic Institute of Porto, Porto, Portugal

    José António Tenreiro Machado

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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: Agarwal, P., Baleanu, D., Chen, Y., Momani, S., Machado, J. (eds) Fractional Calculus. ICFDA 2018. Springer Proceedings in Mathematics & Statistics, vol 303. Springer, Singapore. https://doi.org/10.1007/978-981-15-0430-3_9

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