3 papers
math.AP2025
Fractional Sobolev spaces and fractional -Laplace equations on locally finite graphs
Mengjie Zhang, Yong Lin, Yunyan Yang
Graph-based analysis holds both theoretical and applied significance, attracting considerable attention from researchers and yielding abundant results in recent years. However, res…
math.AP2025
Fractional Laplace operator and related Schrödinger equations on locally finite graphs
Mengjie Zhang, Yong Lin, Yunyan Yang
In this paper, we first define a discrete version of the fractional Laplace operator through the heat semigroup on a stochastically complete, connected, locally finite…
math.AP2025
Fractional Laplace operator on finite graphs
Mengjie Zhang, Yong Lin, Yunyan Yang
Nowadays a great attention has been focused on the discrete fractional Laplace operator as the natural counterpart of the continuous one. In this paper, we discretize the fractiona…