Self-similar solutions for the fractional viscous Burgers equation in Marcinkiewicz spaces

The aim of this paper is to study the existence of self-similar solutions to the Cauchy problem for the viscous Burgers fractional equation with initial conditions in Marcinkiewcz spaces \(L^{(p,\infty )}\) $L^{(p,\infty )}$ . In particular, we obtain the decay of the Mittag–Leffler family associated with the linear problem in Marcinkiewcz spaces and of its gradient.