Multistep Approach for Nonlinear Fractional Bloch System Using Adomian Decomposition Techniques

  • Asad Freihat
  • Shatha Hasan
  • Mohammed Al-Smadi
  • Omar Abu Arqub
  • Shaher MomaniEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 303)


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.


Multistep approach Fractional system Bolch equations Adomian decomposition method 


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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Asad Freihat
    • 1
  • Shatha Hasan
    • 1
  • Mohammed Al-Smadi
    • 1
  • Omar Abu Arqub
    • 2
  • Shaher Momani
    • 2
    • 3
    Email author
  1. 1.Department of Applied ScienceAjloun College, Al-Balqa Applied UniversityAjlounJordan
  2. 2.Department of Mathematics, Faculty of ScienceJordan UniversityAmmanJordan
  3. 3.Department of Mathematics and SciencesCollege of Humanities and Sciences, Ajman UniversityAjmanUAE

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