In this article, we deal with the existence of non-negative solutions of the class of following non local problem {−M(∫Rn∫Rn|u(x)−u(y)|ns|x−y|2ndxdy)(−Δ)n/ssu=(∫ΩG(y,u)|x−y|μdy)g(x,u)inΩ,u=0inRn∖Ω, where (−Δ)n/ss is the n/ s-fractional Laplace operator, n≥ 1 , s∈ (0 , 1) such that n/ s≥ 2 , Ω ⊂ Rn is a bounded domain with Lipschitz boundary, M: R+→ R+ and g: Ω × R→ R are continuous functions, where g behaves like exp(|u|nn−s) as | u| → ∞. The key feature of this article is the presence of Kirchhoff model along with convolution type nonlinearity having exponential growth which appears in several physical and biological models. © 2021, The Author(s), under exclusive licence to Springer Nature B.V.}, author_keywords={Choquard nonlinearity; Doubly non local problems; Kirchhoff equation; Trudinger-Moser nonlinearity}, keywords={Applications; Mathematical techniques, Biological models; Continuous functions; Exponential growth; Fractional Laplacian; Kirchhoff equation; Lipschitz boundary; Non-negative solutions; Nonlocal problems, Laplace transforms}, funding_details={Department of Science and Technology, Ministry of Science and Technology, IndiaDepartment of Science and Technology, Ministry of Science and Technology, India, डीएसटी, ECR/2017/002651}, funding_details={Science and Engineering Research BoardScience and Engineering Research Board, SERB}, funding_text_1={This research is supported by Science and Engineering Research Board, Department of Science and Technology, Government of India, Grant number: ECR/2017/002651. The second author wants to thank Bennett University for its hospitality during her visit there.}, funding_text_2={This research is supported by Science and Engineering Research Board, Department of Science and Technology, Government of India, Grant number: ECR/2017/002651. The second author wants to thank Bennett University for its hospitality during her visit there.}, references={Alves, C.O., Yang, M., Existence of solutions for a nonlocal variational problem in R2 with exponential critical growth (2017) J. Convex Anal., 24 (4), pp. 1197-1215; Alves, C.O., Cassani, D., Tarsi, C., Yang, M., Existence and concentration of ground state solutions for a critical nonlocal Schrödinger equation in R2 (2016) J. Differ. Equ., 261 (3), pp. 1933-1972; Applebaum, D., Lévy processes—from probability to finance and quantum groups (2004) Not. Am. Math. Soc., 51 (11), pp. 1336-1347; Arora, R., Giacomoni, J., Mukherjee, T., Sreenadh, K., n -Kirchhoff-Choquard equations with exponential nonlinearity (2019) Nonlinear Anal., 108, pp. 113-144; Brasco, L., Lindgren, E., Parini, E., The fractional Cheeger problems (2014) Interfaces Free Bound., 16, pp. 419-458; Brasco, L., Parini, E., Squassina, M., Stability of variational eigenvalues for the fractional p -Laplacian (2016) Discrete Contin. Dyn. Syst., 36, pp. 439-455; Brezis, H., (2011) Functional Analysis, Sobolev Spaces and Partial Differential Equations, , Universitext, Springer, New York; Caffarelli, L., Non-local diffusions, drifts and games (2012) Nonlinear Partial Differential Equations, 7, pp. 37-52. , Abel Symp., Springer, Heidelberg; Caffarelli, L., Silvestre, L., An extension problem related to the fractional Laplacian (2007) Commun. Partial Differ. Equ., 32 (7-9), pp. 1245-1260; Di Nezza, E., Palatucci, G., Valdinoci, E., Hitchhiker’s guide to the fractional Sobolev spaces (2012) Bull. Sci. Math., 136 (5), pp. 521-573; Giacomoni, J., Mishra, P.K., Sreenadh, K., Fractional elliptic equations with critical exponential nonlinearity (2016) Adv. Nonlinear Anal., 5 (1), pp. 57-74; Giacomoni, J., Mishra, P.K., Sreenadh, K., Fractional Kirchhoff equation with critical exponential nonlinearity (2016) Complex Var. Elliptic Equ., 61 (9), pp. 1241-1266; Goyal, S., Sreenadh, K., Nehari manifold for non-local elliptic operator with concave-convex nonlinearities and sign-changing weight functions (2015) Proc. Indian Acad. Sci. Math. Sci., 125 (4), pp. 545-558; Kirchhoff, G., (1876) Mechanik. Vorlesungen über mathematische Physik, , Teubner, Leipzig; Li, F., Gao, C., Zhu, X., Existence and concentration of sign-changing solutions to Kirchhoff-type system with Hartree-type nonlinearity (2017) J. Math. Anal. Appl., 448, pp. 60-80; Lieb, E.H., Existence and uniqueness of the minimizing solution of Choquard nonlinear equation (1976) Stud. Appl. Math, 57, pp. 93-105; Lieb, E.H., Loss, M., (2001) Analysis, 14. , 2, Graduate Studies Mathematics, Am. Math. Soc., Providence; Lü, D., A note on Kirchhoff-type equations with Hartree-type nonlinearities (2014) Nonlinear Anal., 99, pp. 35-48; Martinazzi, L., Fractional Adams-Moser-Trudinger type inequalities (2015) Nonlinear Anal., 127, pp. 263-278; Moroz, V., Schaftingen, J.V., A guide to the Choquard equation (2017) J. Fixed Point Theory Appl., 19 (1), pp. 773-813; Parini, E., Ruf, B., On the Moser-Trudinger inequality in fractional Sobolev-Slobodeckij spaces (2018) Atti Accad. Naz. Lincei, Rend. Lincei, Mat. Appl., 29 (2), pp. 315-319; Pekar, S., (1954) Untersuchung über die Elektronentheorie der Kristalle, , Akademie Verlag, Berlin; Perera, K., Squassina, M., Yang, Y., Bifurcation and multiplicity results for critical fractional p -Laplacian problems (2016) Math. Nachr., 289 (2-3), pp. 332-342; Pucci, P., Xiang, M., Zhang, B., Existence results for Schödinger-Choquard-Kirchhoff equations involving the fractional p -Laplacian (2019) Adv. Calc. Var., 12 (3), pp. 253-275; Servadei, R., Valdinoci, E., Mountain pass solutions for non-local elliptic operators (2012) J. Math. Anal. Appl., 389 (2), pp. 887-898; Xiang, M., Zhang, B., Repovs, D., Existence and multiplicity of solutions for fractional Schrödinger-Kirchhoff equations with Trudinger-Moser nonlinearity (2018) Nonlinear Anal., 186, pp. 74-98; Xiang, M., Rădulescu, V.D., Zhang, B., Fractional Kirchhoff problems with critical Trudinger-Moser nonlinearity (2019) Calc. Var. Partial Differ. Equ., 58 (2)}, correspondence_address1={Mukherjee, T.; Department of Mathematics, India; email: tulimukh@gmail.com}, publisher={Springer Science and Business Media B.V.}, issn={01678019}, coden={AAMAD}, language={English}, abbrev_source_title={Acta Appl Math}, document_type={Article}, source={Scopus},