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Stability of a time fractional advection-diffusion system

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  • Arfaoui, Hassen
  • Ben Makhlouf, Abdellatif

Abstract

In this paper, we consider a one dimensional advection-diffusion system in Caputo fractional order derivative. Using a Fourier decomposition and the Mittag-Leffler Function (MLF), we prove a new stability results for the solution of a such system. Numerical experiments were carried out at the end of this work to confirm the theoretical results obtained.

Suggested Citation

  • Arfaoui, Hassen & Ben Makhlouf, Abdellatif, 2022. "Stability of a time fractional advection-diffusion system," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    • Handle: RePEc:eee:chsofr:v:157:y:2022:i:c:s096007792200159x
    DOI: 10.1016/j.chaos.2022.111949
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    1. Ghanbari, Behzad & Günerhan, Hatıra & Srivastava, H.M., 2020. "An application of the Atangana-Baleanu fractional derivative in mathematical biology: A three-species predator-prey model," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    2. Salahshour, Soheil & Ahmadian, Ali & Allahviranloo, Tofigh, 2021. "A new fractional dynamic cobweb model based on nonsingular kernel derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    3. Singh, Jagdev & Kumar, Devendra & Hammouch, Zakia & Atangana, Abdon, 2018. "A fractional epidemiological model for computer viruses pertaining to a new fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 504-515.
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    1. Arfaoui, Hassen & Ben Makhlouf, Abdellatif, 2022. "Stability of a fractional advection–diffusion system with conformable derivative," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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