KARABADJI Nour El Islem (Co-Auteur)2025-09-162025-09-162024-09http://dspace.ensti-annaba.dz:4000/handle/123456789/832https://doi.org/10.3390/ 2024, 13, 653.In this study, we introduce a novel local fractional integral identity related to the Gaussian two-point left Radau rule. Based on this identity, we establish some new fractal inequalities for functions whose first-order local fractional derivatives are generalized convex and concave. The obtained results not only represent an extension of certain previously established findings to fractal sets but also a refinement of these when the fractal dimension μ is equal to one. Finally, to support our findings, we present a practical application to demonstrate the effectiveness of our results.enArticle