This article concerns about the existence and multiplicity of weak solutions for the following nonlinear doubly nonlocal problem with critical nonlinearity in the sense of Hardy–Littlewood–Sobolev inequality {(−Δ)su=λ|u|q−2u+(∫Ω[Formula presented]dy)|u|2μ ⁎−2uinΩ(−Δ)sv=δ|v|q−2v+(∫Ω[Formula presented]dy)|v|2μ ⁎−2vinΩu=v=0inRn∖Ω where Ω is a smooth bounded domain in Rn, n>2s, s∈(0,1), (−Δ)s is the well known fractional Laplacian, μ∈(0,n), 2μ ⁎=[Formula presented] is the upper critical exponent in the Hardy–Littlewood–Sobolev inequality, 1<q<2 and λ,δ>0 are real parameters. We study the fibering maps corresponding to the functional associated with (Pλ,δ) and show that minimization over suitable subsets of Nehari manifold renders the existence of at least two non trivial solutions of (Pλ,δ) for suitable range of λ and δ. © 2018 Elsevier Inc.}, author_keywords={Choquard equation; Fractional Laplacian; Hardy–Littlewood–Sobolev critical exponent; Nonlocal operator}, funding_details={Indo-French Centre for Applied MathematicsIndo-French Centre for Applied Mathematics, IFCAM, UMI CNRS 3494}, funding_text_1={The authors were funded by IFCAM (Indo-French Centre for Applied Mathematics) UMI CNRS 3494 under the project “Singular phenomena in reaction diffusion equations and in conservation laws”.}, references={Alves, C.O., Figueiredo, M.G., Yang, M., Existence of solutions for a nonlinear Choquard equation with potential vanishing at infinity (2016) Adv. 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Differential Equations, 260 (2), pp. 1392-1413; Zhang, X., Zhang, B., Xiang, M., Ground states for fractional Schrödinger equations involving a critical nonlinearity (2016) Adv. Nonlinear Anal., 5 (3), pp. 293-314}, correspondence_address1={Giacomoni, J.; Université de Pau et des Pays de l'Adour, avenue de l'université, France; email: jacques.giacomoni@univ-pau.fr}, publisher={Academic Press Inc.}, issn={0022247X}, language={English}, abbrev_source_title={J. Math. Anal. Appl.}, document_type={Article}, source={Scopus},