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Iterative Analysis of Nonlinear BBM Equations under Nonsingular Fractional Order Derivative

Author

Listed:
  • Gauhar Ali
  • Israr Ahmad
  • Kamal Shah
  • Thabet Abdeljawad

Abstract

The present research work is devoted to investigate fractional order Benjamin‐Bona‐Mahony (FBBM) as well as modified fractional order FBBM (FMBBM) equations under nonlocal and nonsingular derivative of Caputo‐Fabrizio (CF). In this regards, some qualitative results including the existence of at least one solution are established via using some fixed point results of Krasnoselskii and Banach. Further on using an iterative method, some semianalytical results are also studied. The concerned tool is formed when the Adomian decomposition method is coupled with some integral transform like Laplace. Graphical presentations are given for various fractional orders. Also, the concerned method is also compared with some variational‐type perturbation method to demonstrate the efficiency of the proposed method.

Suggested Citation

  • Gauhar Ali & Israr Ahmad & Kamal Shah & Thabet Abdeljawad, 2020. "Iterative Analysis of Nonlinear BBM Equations under Nonsingular Fractional Order Derivative," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).
    • Handle: RePEc:wly:jnlamp:v:2020:y:2020:i:1:n:3131856
    DOI: 10.1155/2020/3131856
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    References listed on IDEAS

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    1. Shah, Kamal & Alqudah, Manar A. & Jarad, Fahd & Abdeljawad, Thabet, 2020. "Semi-analytical study of Pine Wilt Disease model with convex rate under Caputo–Febrizio fractional order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
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