Neutrosophic Riemann integration and its properties

Biswas, Suvankar; Moi, Sandip; Sarkar, Subhadeep

doi:10.1007/s00500-021-06200-7

Cited by 9 publications

(5 citation statements)

References 25 publications

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“…for all L, M ∈ N n , 0 ≤ ζ, η, θ ≤ 1 and g is continuous. Also, for any L, M ∈ N n and λ ∈ R we can show that (see Biswas et al [38])…”

Section: The Truth Membership Function T(mentioning

confidence: 94%

“…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]. Rahaman et al [39] established the approach for solving linear and quadratic equations using Cauchy neutrosophic coefficients.…”

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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“…for all L, M ∈ N n , 0 ≤ ζ, η, θ ≤ 1 and g is continuous. Also, for any L, M ∈ N n and λ ∈ R we can show that (see Biswas et al [38])…”

Section: The Truth Membership Function T(mentioning

confidence: 94%

Section: Neutrosophic Calculus and Differential Equationmentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

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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“…Fourth, rewrite this solution by decomposition infinite series as, (20) then, (21) Fifth, rewrite the equation in (fourth) as recursive equations: (22) Now one can calculate ( approximation solution by using Eq. (11), where the exact solution will be limited to approximation when k goes to infinite.…”

Section: Algorithm Of Decomposition Methodsmentioning

confidence: 99%

Decomposing Method for Space-Time Fractional Order PDEs

Shukur,

Jaber,

RASHEED

et al. 2024

AJEST

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Numerical solutions to integer-order differential equations frequently employ decomposition as one of many methods. This paper provides a generalization of integer-order differential equations into fractional order, which is more general, as well as generalizing the decomposing method into the fractional case and then applying it to solve differential equations of fractional order in both space and time. A fractional calculus's theorems and properties to generalize both differential equations and the decomposition method have been utilized. This method to solve different fractional time and space partial differential equations, demonstrating its ability and applicability to various problems have been applied. The method to various cases to highlight its strengths has been used. The graphs and tables of results obtained using Matlab programs have been presented and discussed.

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“…Te notion of neutrosophic sets (NS) was frst put forth by Smarandache in [3]. Recently, it attracted signifcant attention from researchers working in several felds such as in analysis [4,5], topology [6], algebraic structure [7][8][9], and graph theory [10] as well as applications ranging from sentiment analysis to medical diagnostics [11].…”

Section: Introductionmentioning

confidence: 99%