Existence results of fractional delay differential equations with multi-point boundary conditions via $ \mathbb{L} $–intuitionistic fuzzy mappings

Rehana Tabassum; Mohammed Shehu Shagari; Marriam Anayat; Faryad Ali; Mohammed A. Al-Kadhi; Akbar Azam; Rehana Tabassum; Mohammed Shehu Shagari; Marriam Anayat; Faryad Ali; Mohammed A. Al-Kadhi; Akbar Azam

doi:10.3934/math.20261271

AIMS Mathematics

2026, Volume 11, Issue 10: 32347-32368. doi: 10.3934/math.20261271

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Existence results of fractional delay differential equations with multi-point boundary conditions via $ \mathbb{L} $–intuitionistic fuzzy mappings

1.
Department of Mathematics, Preston University, Islamabad 44000, Pakistan
2.
Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria
3.
Department of Mathematics, COMSATS University, Islamabad 44000, Pakistan
4.
Department of Mathematics and Statistics, College of Science, Imam Mohammad, Ibn Saud Islamic University, Riyadh 11623, Saudi Arabia
5.
Department of Mathematics, Grand Asian University, Sialkot, 7KM, Pasrur Road, 51310, Sialkot, Pakistan

Received: 21 May 2026 Revised: 26 July 2026 Accepted: 03 August 2026 Published: 08 October 2026
MSC : 34A12, 46S40, 47H10, 54H25

This paper introduces a novel concept termed $ \mathbb{L} $–intuitionistic fuzzy mapping and studies the corresponding $ \mathbb{L} $–intuitionistic fuzzy fixed point theorems within the context of a $ (\mathbb{T}, \mathbb{N}, \alpha_{\mathbb{L}}) $–level set. These notions are further employed to establish common $ \mathbb{L} $–intuitionistic fuzzy fixed point results using hybrid-type contraction on $ b $-metric space. Some important special cases are emphasized and examined as corollaries to indicate the generality of the ideas proposed herein. The hypotheses of the main results are confirmed through nontrivial examples. Additionally, a graphical representation is included to visually depict the newly introduced notion. Furthermore, utilizing one of the outcomes presented, new solvability criteria for a class of fractional delay differential equations subject to multi-point boundary conditions are provided.
Citation: Rehana Tabassum, Mohammed Shehu Shagari, Marriam Anayat, Faryad Ali, Mohammed A. Al-Kadhi, Akbar Azam. Existence results of fractional delay differential equations with multi-point boundary conditions via $ \mathbb{L} $–intuitionistic fuzzy mappings[J]. AIMS Mathematics, 2026, 11(10): 32347-32368. doi: 10.3934/math.20261271

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Abstract

This paper introduces a novel concept termed $ \mathbb{L} $–intuitionistic fuzzy mapping and studies the corresponding $ \mathbb{L} $–intuitionistic fuzzy fixed point theorems within the context of a $ (\mathbb{T}, \mathbb{N}, \alpha_{\mathbb{L}}) $–level set. These notions are further employed to establish common $ \mathbb{L} $–intuitionistic fuzzy fixed point results using hybrid-type contraction on $ b $-metric space. Some important special cases are emphasized and examined as corollaries to indicate the generality of the ideas proposed herein. The hypotheses of the main results are confirmed through nontrivial examples. Additionally, a graphical representation is included to visually depict the newly introduced notion. Furthermore, utilizing one of the outcomes presented, new solvability criteria for a class of fractional delay differential equations subject to multi-point boundary conditions are provided.

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