doi:10.1142/S1793557122502035engIslam, Md. N.Kaish, I.Akhtar, Md. N.Navascués, M. A.Fractal Sobolev systems of functions associated with orthonormal systems of functionsART-2022-131384This paper introduces the α-fractal Sobolev system of functions corresponding to Sobolev orthonormal system of functions. An approximation-related result similar to Weierstrass theorem is derived. It is shown that the set of α-fractal versions of Sobolev sums is dense and complete in the weighted Sobolev space Wr,2ρ(I). A Schauder basis and a Riesz basis of fractal type for the space Wr,2ρ(I) are found. The Fourier–Sobolev expansion of an α-fractal function fα corresponding to a certain set of interpolation points is presented. Moreover, some results on convergence of Fourier–Sobolev expansion of fα with respect to uniform norm and Sobolev norm are established.2022http://zaguan.unizar.es/record/12434810.1142/S1793557122502035http://zaguan.unizar.es/record/124348oai:zaguan.unizar.es:124348Asian-European Journal of Mathematics 15, 11 (2022)All rights reservedhttp://www.europeana.eu/rights/rr-f/info:eu-repo/semantics/openAccess