Riesz fractional integral

The Riesz fractional integral is a mathematical tool that extends the idea of traditional integration, allowing us to analyze functions with a fractional (non-integer) degree of accumulation or smoothing. Unlike regular integrals, which measure the total area under a curve, fractional integrals capture more nuanced, intermediate behaviors between no integration and full integration. The Riesz version specifically operates in multiple dimensions, smoothing functions in a way that depends on a fractional order, useful in fields like physics and signal processing to model phenomena with complex or non-local interactions, reflecting a balance between local and global features.