In this article we investigate the solution of the steady-state fractional diffusion equation on a bounded domain in ℝ¹. The diffusion operator investigated, motivated by physical considerations, is ...

Aggregation-diffusion equations and gradient flows form a dynamic field of study at the intersection of mathematical analysis, statistical mechanics and applied physics. These equations characterise ...

Green's functions and propagators for the multi-dimensional anisotropic space-time fractional diffusion equation are obtained in integral form. Uniqueness of the solutions is studied in the framework ...

Observing nature shows that many temporal and spatial structures are not formed by the outside, but rather by the respective system itself. To study these self-organizing processes is the subject of ...

This paper develops two local mesh-free methods for designing stencil weights and spatial discretization, respectively, for parabolic partial differential equations (PDEs) of ...

A groundbreaking mathematical equation has been discovered, which could transform medical procedures, natural gas extraction, and plastic packaging production in the future. The new equation, ...