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

Alaa Fouad Momena (), Rakibul Haque, Mostafijur Rahaman, Soheil Salahshour and Sankar Prasad Mondal
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Alaa Fouad Momena: Department of Industrial Engineering, College of Engineering, Prince Sattam Bin Abdulaziz University, Al Kharj 11942, Saudi Arabia
Rakibul Haque: Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, Haringhata 741249, West Bengal, India
Mostafijur Rahaman: Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, West Bengal, India
Soheil Salahshour: Faculty of Engineering and Natural Sciences, Istanbul Okan University, 34959 Istanbul, Turkey
Sankar Prasad Mondal: Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, Haringhata 741249, West Bengal, India

Logistics, 2024, vol. 8, issue 1, 1-28

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.

Keywords: neutrosophic set; generalized neutrosophic derivative; neutrosophic differential equation; existence and uniqueness theorem; inventory control problem; price and stock dependent demand (search for similar items in EconPapers)
JEL-codes: L8 L80 L81 L86 L87 L9 L90 L91 L92 L93 L98 L99 M1 M10 M11 M16 M19 R4 R40 R41 R49 (search for similar items in EconPapers)
Date: 2024
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