Second-order neutrosophic boundary-value problem

Moi, Sandip; Biswas, Suvankar; Pal, Sanjay Kumar

doi:10.1007/s40747-020-00268-8

Cited by 6 publications

(2 citation statements)

References 31 publications

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“…Moi et al [36] proposed the notion of a "generalized neutrosophic derivative" of a neutrosophic-valued function and discussed the solving approach of linear NDE. After that, Moi et al [37] analyzed a neutrosophic boundary value problem using a different type of generalized neutrosophic derivative. The notion of neutrosophic Riemann integration is established by Biswas et al [38].…”

Section: Neutrosophic Calculus and Differential Equationmentioning

confidence: 99%

“…It has come to our attention that the majority of studies [9,[34][35][36][37][38][39][41][42][43][44][45][46][47]49,50] in neutrosophic set theory have focused on applying neutrosophic sets in various scientific disciplines. However, there has been minimal effort directed towards the comprehensive development of neutrosophic differential equations and their manifestation within the neutrosophic context.…”

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confidence: 99%

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The Existence and Uniqueness Conditions for Solving Neutrosophic Differential Equations and Its Consequence on Optimal Order Quantity Strategy

Momena,

Haque,

Rahaman

et al. 2024

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Background: Neutrosophic logic explicitly quantifies indeterminacy while also maintaining the independence of truth, indeterminacy, and falsity membership functions. This characteristic assumes an imperative part in circumstances, where dealing with contradictory or insufficient data is a necessity. The exploration of differential equations within the context of uncertainty has emerged as an evolving area of research. Methods: the solvability conditions for the first-order linear neutrosophic differential equation are proposed in this study. This study also demonstrates both the existence and uniqueness of a solution to the neutrosophic differential equation, followed by a concise expression of the solution using generalized neutrosophic derivative. As an application of the first-order neutrosophic differential equation, we discussed an economic lot sizing model in a neutrosophic environment. Results: This study finds the conditions for the existing solution of a first-order neutrosophic differential equation. Through the numerical simulation, this study also finds that the neutrosophic differential equation approach is much better for handling uncertainty involved in inventory control problems. Conclusions: This article serves as an introductory exploration of differential equation principles and their application within a neutrosophic environment. This approach can be used in any operation research or decision-making scenarios to remove uncertainty and attain better outcomes.

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Section: Neutrosophic Calculus and Differential Equationmentioning

confidence: 99%

mentioning

confidence: 99%

The Existence and Uniqueness Conditions for Solving Neutrosophic Differential Equations and Its Consequence on Optimal Order Quantity Strategy

Momena,

Haque,

Rahaman

et al. 2024

Logistics

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Neutrosophic Riemann integration and its properties

2021

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Numerical integration of neutrosophic valued function by Gaussian quadrature methods

2022

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In this article, different types of Gaussian quadrature methods have been presented to find the numerical integration of a neutrosophic valued function. A new definition of the distance between two neutrosophic number has been defined and it has been proved that the distance and the set of all neutrosophic number form a complete metric space. Also, the definition of neutrosophic continuity on a closed-bounded interval has been defined in the sense of $$(\alpha ,\beta ,\gamma )$$ ( α , β , γ ) -cut. This is the first time, when the Gauss–Legendre integration, Gauss–Chebyshev integration and Gauss–Laguerre integration rule have been discussed in neutrosophic environment. In the first test example, the comparison between one-point, two-point and three-point Gauss–Legendre integration rules have been presented in terms of tables and figures. Also, in the second example, the comparison between one-point, two-point Gauss–Chebyshev and Gauss–Laguerre integration rules have been discussed.

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Second-order neutrosophic boundary-value problem

Cited by 6 publications

References 31 publications

The Existence and Uniqueness Conditions for Solving Neutrosophic Differential Equations and Its Consequence on Optimal Order Quantity Strategy

The Existence and Uniqueness Conditions for Solving Neutrosophic Differential Equations and Its Consequence on Optimal Order Quantity Strategy

Neutrosophic Riemann integration and its properties

Numerical integration of neutrosophic valued function by Gaussian quadrature methods

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