Transmission problems for the fractional $ p $-Laplacian across fractal interfaces

We consider a parabolic transmission problem, involving nonlinear fractional operators of different order, across fractal interface \begin{document}$ \Sigma $\end{document}. The condition is Robin type and it involves the jump id="M3">\begin{document}$ p $\end{document}-fractional normal derivatives on irregular interface. After proving existence uniqueness results for weak solution problem at hand, via semigroup approach, we investigate regularity semigroup.