Colombeau theory of generalized function with Leibniz’s rule

Abstract

To reveal some fundamental facts at the interaction among mathematics and the modern real world, putting in verification mathematical entities like “nonlinear generalized functions” that are required to model the modern era. In this present paper, some artefacts of distributions are illustrated. The repercussions are derived in Colombeau theory of nonlinear generalized functions, which is the quite pertinent algebraic construction for dealing with Schwartz distributions. Colombeau theory of nonlinear generalized function ₢(R) contains the space ₷(R) of Schwartz distributions as a subspace, and has a notion of mathematical ‘association’ that permits us to assess the outcomes in terms of distributions.