2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/171052In the paper, the large time behavior of solutions of the Cauchy problem for the one dimensional fractal Burgers equation $u_t+(-\partial^2_x)^{α/2} u+uu_x=0$ with $α\in (1,2)$ is studied. It is shown that if the nondecreasing initial datum approaches the constant states $u_\pm$ ($u_-<u_+$) as $x\to \pm\infty$, respectively, then the corresponding solution converges toward the rarefaction wave, {\it i.e.} the unique entropy solution of the Riemann problem for the nonviscous Burgers equation.15 pagesAnalysis of PDEs60J60, 35B40,35K55,35Q53text