doi:10.1140/epjs/s11734-023-00865-xengBanerjee, AkashAkhtar, Md. NasimNavascués, M. A.Local a -fractal interpolation functionART-2023-134338Constructions of the (global) fractal interpolation functions on standard function spaces got a lot of attention in the last centuries. Motivated by the newly introduced local fractal functions corresponding to a local iterated functions system which is the generalization of the traditional iterated functions system we construct the local non-affine α - fractal functions in this article. A few examples of the graphs of these functions are provided. A fractal operator which takes the classical function to its local fractal counterpart is defined and some of its properties are also studied.2023http://zaguan.unizar.es/record/12691310.1140/epjs/s11734-023-00865-xhttp://zaguan.unizar.es/record/126913oai:zaguan.unizar.es:126913European Physical Journal-Special Topics 232, 7 (2023), 1043-1050byhttp://creativecommons.org/licenses/by/3.0/es/info:eu-repo/semantics/openAccess