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Résumé : In this article, we are devoted to studying the following nonlocal Navier–Stokes equations involving the time–space fractional operators { ∂ t β u + ( − Δ ) α u + u ⋅ ∇ u = ∇ p + λ | u | q − 2 u + g ( x , t ) in Ω × R + , div u = 0 in Ω × R + , u ( x , t ) = 0 in ( R N ∖ Ω ) × R + ,