fracpartial

Fracpartial is a term that sometimes appears in discussions related to fractional calculus. Fractional calculus is a branch of mathematical analysis that generalizes the concept of differentiation and integration to non-integer orders. Instead of taking the first derivative or the second derivative, one might consider a derivative of order 1/2 or pi. The notation "fracpartial" is not a standard, universally recognized symbol in the mathematical community. It appears to be a portmanteau of "fractional" and "partial derivative."

Partial derivatives are used in multivariable calculus to describe how a function changes with respect to one of its variables, while holding others constant. For example, the partial derivative of a function f(x, y) with respect to x is denoted as ∂f/∂x. When discussing fractional calculus in the context of multivariable functions, one might encounter generalized concepts that could be informally referred to as fractional partial derivatives. However, there isn't a single, standardized symbol like ∂^αf/∂x^α where α is a fractional number that is universally called "fracpartial."

The actual notation for fractional partial derivatives can vary depending on the specific definition of fractional derivative being used (e.g., Riemann-Liouville, Caputo, Grünwald-Letnikov) and the context of the problem. Researchers in fractional calculus may develop their own specific notations for clarity within their work, and "fracpartial" might arise in such informal settings or in discussions seeking a shorthand. However, for formal mathematical literature, it's more common to see explicit references to the type of fractional derivative and the order.