2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/193886We consider an anisotropic brane world with Bianchi type I and V geometries where the mechanism of confining the matter on the brane is through the use of a confining potential. The resulting equations on the anisotropic brane are modified by an extra term that may be interpreted as the x-matter, providing a possible phenomenological explanation for the accelerated expansion of the universe. We obtain the general solution of the field equations in an exact parametric form for both Bianchi type I and V space-times. In the special case of a Bianchi type I the solutions of the field equations are obtained in an exact analytic form. Finally, we study the behavior of the observationally important parameters.14 pages, 3 figures, to appear in PLBGeneral Relativity and Quantum CosmologyHigh Energy Physics - Theorytext