Neutrosophic Precalculus and Neutrosophic Calculus

TL;DR

This paper introduces the concepts of neutrosophic precalculus and calculus, extending classical analysis to handle indeterminacy and uncertainty, and proposes new definitions like neutrosophic mereo-limit and neutrosophic mereo-continuity.

Contribution

It presents the first definitions of neutrosophic mereo-limit, mereo-continuity, mereo-derivative, and mereo-integral, expanding neutrosophic analysis beyond existing frameworks.

Findings

Introduced neutrosophic mereo-limit and mereo-continuity concepts.

Defined neutrosophic mereo-derivative and mereo-integral.

Highlighted the potential for further research in neutrosophic fractional calculus.

Abstract

Neutrosophic Analysis is a generalization of Set Analysis, which in its turn is a generalization of Interval Analysis. Neutrosophic Precalculus is referred to indeterminate staticity, while Neutrosophic Calculus is the mathematics of indeterminate change. The Neutrosophic Precalculus and Neutrosophic Calculus can be developed in many ways, depending on the types of indeterminacy one has and on the methods used to deal with such indeterminacy. In this book, the author presents a few examples of indeterminacies and several methods to deal with these specific indeterminacies, but many other indeterminacies there exist in our everyday life, and they have to be studied and resolved using similar of different methods. Therefore, more research should to be done in the field of neutrosophics. The author introduces for the first time the notions of neutrosophic mereo-limit, neutrosophic mereo-continuity (in a different way from the classical semi-continuity), neutrosophic mereo-derivative and neutrosophic mereo-integral (both in different ways from the fractional calculus), besides the classical definitions of limit, continuity, derivative, and integral respectively. Future research may be done in the neutrosophic fractional calculus.