The Existence and Uniqueness Conditions for Solving Neutrosophic Differential Equations and Its Consequence on Optimal Order Quantity Strategy
<i>Background</i>: 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 d...
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MDPI AG
2024-02-01
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| author | Alaa Fouad Momena Rakibul Haque Mostafijur Rahaman Soheil Salahshour Sankar Prasad Mondal |
| author_facet | Alaa Fouad Momena Rakibul Haque Mostafijur Rahaman Soheil Salahshour Sankar Prasad Mondal |
| author_sort | Alaa Fouad Momena |
| collection | DOAJ |
| description | <i>Background</i>: 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. <i>Methods</i>: 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. <i>Results</i>: 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. <i>Conclusions</i>: 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. |
| first_indexed | 2024-04-24T18:05:07Z |
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| id | doaj.art-a876b68689bd41c783143a6aebb681bc |
| institution | Directory Open Access Journal |
| issn | 2305-6290 |
| language | English |
| last_indexed | 2024-04-24T18:05:07Z |
| publishDate | 2024-02-01 |
| publisher | MDPI AG |
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| spelling | doaj.art-a876b68689bd41c783143a6aebb681bc2024-03-27T13:51:36ZengMDPI AGLogistics2305-62902024-02-01811810.3390/logistics8010018The Existence and Uniqueness Conditions for Solving Neutrosophic Differential Equations and Its Consequence on Optimal Order Quantity StrategyAlaa Fouad Momena0Rakibul Haque1Mostafijur Rahaman2Soheil Salahshour3Sankar Prasad Mondal4Department of Industrial Engineering, College of Engineering, Prince Sattam Bin Abdulaziz University, Al Kharj 11942, Saudi ArabiaDepartment of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, Haringhata 741249, West Bengal, IndiaDepartment of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, West Bengal, IndiaFaculty of Engineering and Natural Sciences, Istanbul Okan University, 34959 Istanbul, TurkeyDepartment of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, Haringhata 741249, West Bengal, India<i>Background</i>: 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. <i>Methods</i>: 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. <i>Results</i>: 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. <i>Conclusions</i>: 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.https://www.mdpi.com/2305-6290/8/1/18neutrosophic setgeneralized neutrosophic derivativeneutrosophic differential equationexistence and uniqueness theoreminventory control problemprice and stock dependent demand |
| spellingShingle | Alaa Fouad Momena Rakibul Haque Mostafijur Rahaman Soheil Salahshour Sankar Prasad Mondal The Existence and Uniqueness Conditions for Solving Neutrosophic Differential Equations and Its Consequence on Optimal Order Quantity Strategy Logistics neutrosophic set generalized neutrosophic derivative neutrosophic differential equation existence and uniqueness theorem inventory control problem price and stock dependent demand |
| title | The Existence and Uniqueness Conditions for Solving Neutrosophic Differential Equations and Its Consequence on Optimal Order Quantity Strategy |
| title_full | The Existence and Uniqueness Conditions for Solving Neutrosophic Differential Equations and Its Consequence on Optimal Order Quantity Strategy |
| title_fullStr | The Existence and Uniqueness Conditions for Solving Neutrosophic Differential Equations and Its Consequence on Optimal Order Quantity Strategy |
| title_full_unstemmed | The Existence and Uniqueness Conditions for Solving Neutrosophic Differential Equations and Its Consequence on Optimal Order Quantity Strategy |
| title_short | The Existence and Uniqueness Conditions for Solving Neutrosophic Differential Equations and Its Consequence on Optimal Order Quantity Strategy |
| title_sort | existence and uniqueness conditions for solving neutrosophic differential equations and its consequence on optimal order quantity strategy |
| topic | neutrosophic set generalized neutrosophic derivative neutrosophic differential equation existence and uniqueness theorem inventory control problem price and stock dependent demand |
| url | https://www.mdpi.com/2305-6290/8/1/18 |
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