A study on intuitionistic fuzzy neutral functional integro-differential PDEs with impulses

Q1 Mathematics

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-01 DOI:10.1016/j.padiff.2025.101296

T. Gunasekar , K. Nithyanandhan , Hanumagowda B. N , Jagadish V. Tawade , Nashwan Adnan Othman , Barno Abdullaeva , Nadia Batool , Khayrilla Kurbonov

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Abstract

This paper investigates the existence and uniqueness of solutions for a nonlocal intuitionistic fuzzy impulsive integro-differential equation, employing intuitionistic fuzzy semigroups and the contraction mapping principle. Through a systematic theoretical framework, it establishes that, under certain conditions, a distinct solution is ensured. Additionally, the study expands its analysis to explore the existence results for intuitionistic fuzzy impulsive neutral integro-differential equations, broadening its research focus. This approach introduces a new perspective on understanding intuitionistic fuzzy integro-differential equations, introducing innovative methodologies and significant discoveries that advance theoretical exploration in this field. The findings underscore that, subject to specific assumptions, a singular fuzzy solution emerges for these problems marked by nonlocal conditions, effectively addressing crucial challenges in the analysis of fuzzy systems.

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带有脉冲的直觉模糊中立泛函积分微分偏微分方程的研究

利用直觉模糊半群和压缩映射原理，研究了一类非局部直觉模糊脉冲积分微分方程解的存在唯一性。通过系统的理论框架，确立了在一定条件下，保证有一个独特的解。此外，本研究将其分析扩展到探索直觉模糊脉冲中立型积分微分方程的存在性结果，拓宽了研究的重点。这种方法引入了理解直觉模糊积分微分方程的新视角，引入了创新的方法和重大发现，推动了该领域的理论探索。研究结果强调，在特定的假设下，对于这些以非局部条件为特征的问题，一个单一的模糊解决方案出现了，有效地解决了模糊系统分析中的关键挑战。

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