Manuscript Topics

The fractional elliptic and parabolic equations have found wide spread applications in various branches of sciences and have drawn more and more attentions from the mathematical community. They are employed in modeling anomalous diffusion in biological systems, porous media, and materials science.

Additionally, these operators play crucial roles in probability and finance. In particular, the fractional Laplacians can be interpreted as the infinitesimal generator of a stable Levy process.

Overall, fractional elliptic and parabolic equations provide enhanced accuracy in scenarios where classical models fall short or where non-local interactions are crucial and provide a powerful framework for understanding and analyzing complex systems exhibiting anomalous diffusion across various scientific fields.

In this special issue, we invite review and original research articles dealing with recent developments on the analysis of qualitative properties of solutions to nonlinear fractional elliptic and parabolic equations. It will focus on, but not limited to, the following analysis on the solutions of these equations:

Symmetry and monotonicity
Blowing up and rescaling, a priori estimates
Uniqueness, non-existence, classifications of solutions
Regularities of solutions
existence of solutions

Keywords
Fractional Laplacian, non-local operators, elliptic and parabolic equations, nonlinearity, symmetry, monotonicity, blowing up and rescaling, a priori estimate, existence, non-existence, uniqueness, classification, method of moving planes, sliding method.

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