University of Mohaghegh Ardabili Journal of Finsler Geometry and its Applications 2783-0500 7 1 2026 05 01 Shape and topological optimization for a fractional elliptic boundary problem 45 65 4157 10.22098/jfga.2025.17676.1163 EN Malick FALL D´epartement de Math´emtiques, Universit´e Gamal Abdel Nasser de Conakry, FST, BP 1147 Conakry, Guinea Mame Gor NGOM D´epartement de Math´emtiques, Universit´e Gamal Abdel Nasser de Conakry, FST, BP 1147 Conakry, Guinea Guillaume Itbadio Sadio Laboratoire de Math´ematiques et Applications (LMA), Universit´e Assane Seck de Ziguinchor, UFR ST BP 523 Ziguinchor, Senegal Ibrahima Faye Laboratoire d’Informatique, de Math´ematiques et Applications (LIMA), UFR SATIC, Universit´e Alioune Diop de Bambey, BP 30 Bambey, Senegal Alassane Sy Laboratoire d’Informatique, de Math´ematiques et Applications (LIMA), UFR SATIC, Universit´e Alioune Diop de Bambey, BP 30 Bambey, Senegal Diaraf Seck Laboratoire de Math´ematiques de la D´ecision et d’Analyse Num´erique (L.M.D.A.N).Université Cheikh Anta Diop, Dakar, Senegal Journal Article 2025 06 16 In this paper, we consider a shape optimization problem associated with the fractional Lapla<br />cian We focus on J( Omega) = j( Omega,u ) where u is the solution of 1.3. We give an existence of<br />optimal shape using differents methods. These results are based compactness and <br />cone property. We establish also the shape derivative and topological derivative of the functional<br />using the minmax method. https://jfga.uma.ac.ir/article_4157_473e490ff32c4d544ffdd28a44251ca0.pdf