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Second-order neutrosophic boundary-value problem.

Sandip Moi1, Suvankar Biswas2, Smita Pal Sarkar1

  • 1Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, B. Garden, Howrah, 711103 India.

Complex & Intelligent Systems
|November 15, 2021
PubMed
Summary

This study introduces neutrosophic differential calculus, presenting novel properties of neutrosophic derivatives and numbers. It pioneers the development of second-order neutrosophic boundary-value problems with diverse derivative types.

Keywords:
Generalized neutrosophic derivativeNeutrosophic boundary-value problemNeutrosophic differential calculusSecond-order neutrosophic differential equation

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Area of Science:

  • Mathematics
  • Applied Mathematics
  • Neutrosophic Theory

Background:

  • Neutrosophic theory extends classical set theory and fuzzy logic.
  • The development of calculus based on neutrosophic numbers is an emerging field.
  • Existing literature lacks comprehensive frameworks for neutrosophic differential equations, especially concerning higher-order problems.

Purpose of the Study:

  • To present fundamental properties of neutrosophic derivatives and neutrosophic numbers.
  • To establish the foundations of neutrosophic differential calculus.
  • To introduce and analyze second-order neutrosophic boundary-value problems.

Main Methods:

  • Derivation and analysis of properties for neutrosophic derivatives and numbers.
  • Development of various systems of first- and second-order neutrosophic derivatives.
  • Formulation and examination of a novel second-order neutrosophic boundary-value problem.
  • Application of numerical examples to illustrate the developed neutrosophic differential equation systems.

Main Results:

  • A comprehensive set of properties for neutrosophic derivatives and numbers has been established.
  • A novel framework for neutrosophic differential calculus has been successfully developed.
  • The first-ever second-order neutrosophic boundary-value problem, incorporating diverse derivative types, has been introduced.
  • Numerical examples demonstrate the practical application and behavior of the proposed neutrosophic differential equation systems.

Conclusions:

  • The presented properties and calculus form a robust foundation for neutrosophic differential equations.
  • The introduction of second-order neutrosophic boundary-value problems opens new avenues for research in neutrosophic analysis.
  • The study provides essential tools and insights for solving complex problems using neutrosophic mathematics.