Weak solutions to the time-fractional g-Bénard equations

2020/11/02 by Khalid Akhlil, Akhlil, Khalid, Sultana Ben Aadi +3
Engineering · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fractional Differential Equations Solutions #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #math-ph #math.AP #math.MP

paper · pdf · doi:10.48550/arxiv.2011.01545

16 pages. arXiv admin note: text overlap with arXiv:2006.02865

arxiv created 2020/11/02 · openalex publication_date 2020/11/02 · arxiv updated 2020/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce the g-Bénard equations with time-fractional derivative of order α∈ (0, 1) in domains of \mathbb R². This equations model, the memory-dependent heat conduction of liquids in fractal media considered in g-framework. We aim to study the existence and uniqueness of weak solutions by means of standard techniques from Navier-Stokes equations theory and fractional calculus theory.

Citations

• Weak solutions to the time-fractional g-Navier-Stokes equations and optimal control

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