Application of fixed point theory to synaptic delay differential equations in neural networks

Nehad Abduallah Alhajaji; Afrah Ahmad Noman Abdou; Jamshaid Ahmad; Nehad Abduallah Alhajaji; Afrah Ahmad Noman Abdou; Jamshaid Ahmad

doi:10.3934/math.20241495

AIMS Mathematics

2024, Volume 9, Issue 11: 30989-31009. doi: 10.3934/math.20241495

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Research article

Application of fixed point theory to synaptic delay differential equations in neural networks

Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, Jeddah 21589, Saudi Arabia

Received: 16 September 2024 Revised: 17 October 2024 Accepted: 18 October 2024 Published: 31 October 2024
MSC : 46S40, 47H10, 54H25

The objective of this research is to propose a new concept known as rational ($ \alpha \eta $-$ \psi) $-contractions in the framework of $ \mathcal{F} $-metric spaces and to establish several fixed point theorems. These theorems help to generalize and unify various established fixed point results from the existing literature. To demonstrate the practical effectiveness of our approach, we provide a significant example that confirms our findings. In addition, we introduce a generalized multivalued ($ \alpha $-$ \psi) $-contraction concept in $ \mathcal{F} $-metric spaces and use it to prove fixed point theorems specifically designed for multivalued mappings. To demonstrate the practical utility of our findings, we apply our main results to the solution of synaptic delay differential equations in neural networks.
- fixed point,
- rational ($ \alpha \eta $-$ \psi) $-contractions,
- $ \mathcal{F} $-metric spaces,
- multivalued mappings,
- synaptic delay differential equations
Citation: Nehad Abduallah Alhajaji, Afrah Ahmad Noman Abdou, Jamshaid Ahmad. Application of fixed point theory to synaptic delay differential equations in neural networks[J]. AIMS Mathematics, 2024, 9(11): 30989-31009. doi: 10.3934/math.20241495

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Abstract

The objective of this research is to propose a new concept known as rational ($ \alpha \eta $-$ \psi) $-contractions in the framework of $ \mathcal{F} $-metric spaces and to establish several fixed point theorems. These theorems help to generalize and unify various established fixed point results from the existing literature. To demonstrate the practical effectiveness of our approach, we provide a significant example that confirms our findings. In addition, we introduce a generalized multivalued ($ \alpha $-$ \psi) $-contraction concept in $ \mathcal{F} $-metric spaces and use it to prove fixed point theorems specifically designed for multivalued mappings. To demonstrate the practical utility of our findings, we apply our main results to the solution of synaptic delay differential equations in neural networks.

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