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.

我们处理由分数 N-拉普拉斯算子和分数 Orlicz-Sobolev 空间上函数的时间导数给出的非线性抛物线问题。我们得到的结果表明这些分数 N-拉普拉斯热流存在弱解。我们通过使用近似方法得到这个结果。我们首先从差分N-拉普拉斯问题中获得唯一的逼近弱解序列，然后获得变体逼近弱解的一些序列。接下来我们展示了逼近弱解序列对极限的收敛性，并且逼近弱解序列的极限是该问题的弱解。