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

Author:

Momena Alaa Fouad1,Haque Rakibul2ORCID,Rahaman Mostafijur3ORCID,Salahshour Soheil456,Mondal Sankar Prasad2ORCID

Affiliation:

1. Department of Industrial Engineering, College of Engineering, Prince Sattam Bin Abdulaziz University, Al Kharj 11942, Saudi Arabia

2. Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, Haringhata 741249, West Bengal, India

3. Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, West Bengal, India

4. Faculty of Engineering and Natural Sciences, Istanbul Okan University, 34959 Istanbul, Turkey

5. Faculty of Engineering and Natural Sciences, Bahcesehir University, 34349 Istanbul, Turkey

6. Faculty of Science and Letters, Piri Reis University, Tuzla, 34940 Istanbul, Turkey

Abstract

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.

Funder

Prince Sattam Bin Abdulaziz University

Publisher

MDPI AG

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5. Neutrosophic set-a generalization of the intuitionistic fuzzy set;Smarandache;Int. J. Pure. Appl. Math.,2005

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