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On the solutions of fractional-time wave equation with memory effect involving operators with regular kernel

Author

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  • Cuahutenango-Barro, B.
  • Taneco-Hernández, M.A.
  • Gómez-Aguilar, J.F.

Abstract

In this paper, we give analytical solutions of a fractional-time wave equation with memory effect and frictional memory kernel of Mittag–Leffler type via the Atangana–Baleanu fractional order derivative. The method of separation of variables and the Laplace transform has been used to obtain the exact solutions for the fractional order wave equations. Additionally, we present analytical solutions considering the Caputo–Fabrizio fractional derivative with exponential kernel. We showed that the solutions obtained via Caputo–Fabrizio fractional order derivative were a particular case of the solutions obtained with the new fractional derivative based in the Mittag–Leffler law.

Suggested Citation

  • Cuahutenango-Barro, B. & Taneco-Hernández, M.A. & Gómez-Aguilar, J.F., 2018. "On the solutions of fractional-time wave equation with memory effect involving operators with regular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 283-299.
    • Handle: RePEc:eee:chsofr:v:115:y:2018:i:c:p:283-299
    DOI: 10.1016/j.chaos.2018.09.002
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    References listed on IDEAS

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    Cited by:

    1. Abu Arqub, Omar & Maayah, Banan, 2019. "Modulation of reproducing kernel Hilbert space method for numerical solutions of Riccati and Bernoulli equations in the Atangana-Baleanu fractional sense," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 163-170.
    2. Qureshi, Sania & Bonyah, Ebenezer & Shaikh, Asif Ali, 2019. "Classical and contemporary fractional operators for modeling diarrhea transmission dynamics under real statistical data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    3. Mishra, Jyoti, 2019. "Modified Chua chaotic attractor with differential operators with non-singular kernels," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 64-72.

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