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Stability of a fractional advection–diffusion system with conformable derivative

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  • Arfaoui, Hassen
  • Ben Makhlouf, Abdellatif

Abstract

This paper investigates the stability of fractional advection–diffusion system with conformable derivative in infinite time interval. We have established new exponential stability results for a such system in different Hilbert spaces. Then, thanks to numerical methods for solving systems with conformable derivative, we were able to justify numerically the theoretical results obtained.

Suggested Citation

  • Arfaoui, Hassen & Ben Makhlouf, Abdellatif, 2022. "Stability of a fractional advection–diffusion system with conformable derivative," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    • Handle: RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922008281
    DOI: 10.1016/j.chaos.2022.112649
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    References listed on IDEAS

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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. Arfaoui, Hassen & Ben Makhlouf, Abdellatif, 2022. "Stability of a time fractional advection-diffusion system," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    4. Ghanbari, Behzad & Kumar, Sunil & Kumar, Ranbir, 2020. "A study of behaviour for immune and tumor cells in immunogenetic tumour model with non-singular fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    5. Abdellatif Ben Makhlouf & El-Sayed El-Hady & Salah Boulaaras & Mohamed Ali Hammami & Sundarapandian Vaidyanathan, 2022. "Stability Analysis for Differential Equations of the General Conformable Type," Complexity, Hindawi, vol. 2022, pages 1-6, April.
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