A weak solution for the fractional N-Laplacian flow

We deal with the nonlinear parabolic problems given by the fractional N-Laplacian operator and time derivative of functions on the fractional Orlicz–Sobolev spaces. We get a result which shows existence of a weak solution for these fractional N-Laplacian heat flows. We obtain this result by using the approximation method. We first obtain a unique sequence of the approximating weak solutions from the difference fractional N-Laplacian problems, and then get some sequences of the variant approximating weak solutions. We next show the convergence of the sequences of the approximating weak solutions to the limits and the limit of some sequence of the approximating weak solutions is a weak solution of this problem.